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Sustainable Water Quality Monitoring for Developing Countries in the Context ofMiningMonitoring systems and modellingNhantumbo, Clemencio
2017
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Citation for published version (APA):Nhantumbo, C. (2017). Sustainable Water Quality Monitoring for Developing Countries in the Context of Mining:Monitoring systems and modelling. (1st ed.). Water Resources Engineering, Lund University.
Total number of authors:1
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I
Sustainable Water Quality Monitoring for Developing Countries in the
Context of Mining
II
III
Sustainable Water Quality
Monitoring for Developing Countries
in the Context of Mining
Monitoring systems and modelling
Clemêncio M. Carlos Nhantumbo
DOCTORAL DISSERTATION
by due permission of the Faculty of Engineering, Lund University, Sweden.
To be defended at the Faculty of Engineering, V-building, John Ericssons väg 1,
Lund, room V:B on June 1st, 2017 at 10:15 a.m.
Faculty opponent
Prof. Björn Klöve
IV
V
Organization
LUND UNIVERSITY
Document name:
DOCTORAL THESIS
Water Resources Engineering
Box 118
Date of issue:
2017-06-01
SE-22100 Lund, Sweden
Author
Clemencio Nhantumbo
Sponsoring organization:
Swedish International Development Cooperation (SIDA) and Lars Erik Lundberg Scholarship Foundation
Title and subtitle: Sustainable Water Quality Monitoring for Developing Countries in the Context of Mining - Monitoring systems and modelling
Abstract
Mining, seen as a source of revenue in most developing countries, threatens seriously the environment. Mining impacts the water quality and one of the main problems of mining is acid mine drainage. Low pH and high concentration of heavy metals characterize acid mine drainage. When a stream is impacted by acid mine drainage both human activities and the ecological system are seriously affected.
In Mozambique coal mining is growing faster since 2010 while water quality monitoring programs are not well established and improvements are limited due to lack of skilled people and financial resources. The major coal reserves of Mozambique are located in the riparian area of Zambezi River Basin which is the largest river basin in Southern Africa with 11% of its catchment area in Mozambique. The Zambezi river basin in Mozambique has a high potential for development of human activities and its environment is rich and diversified.
There are water quality monitoring systems already developed and successfully implemented in developed countries. However, these systems are not sustainable for developing countries due to lack of resources. A water quality monitoring system that (1) produces consistent and comparable water quality information; (2) provides feedback to outcomes and goals of the government; and (3) promotes continuous improvement of the water quality, in the context of mining development and under the constraint of lack of human and financial resources, is proposed for the Zambezi River Basin in Mozambique. The system includes two alternative monitoring procedures. It is concluded that the best way forward is to implement the first procedure which improves the current situation by using web-based data sharing and slowly move to the second procedure which is centralized and with one company doing water quality monitoring for the entire river basin in Mozambique.
Modelling is an alternative solution for reducing the cost of monitoring by: (1) estimating difficult and costly to measure parameters based on others which are easily obtained and (2) simulating contamination and reclamation of already impacted streams thus shifting usage of resources to monitor water quality changes in more vulnerable areas. Existing surface water quality models have limitations in simulating contamination of streams by acidic discharges. OTIS and PHREEQ C are used for simulating mixing and transport of non-conservative pollutants but they fail when the task is to simulate pH in streams which are influenced by equilibrium reactions between the alkalinity species interacting with the surrounding environment.
Within the scope of this work two models were developed, model (I) for estimating the concentration of inorganic ions in surface water, and model (II) for simulating pH and alkalinity in streams impacted by acidic discharges.
The model (I) estimates the concentration of major ions (𝑁𝑎+, 𝐾+, 𝑀𝑔2+, 𝐶𝑎2+,𝐻𝐶𝑂3−, 𝑆𝑂4
2−, 𝐶𝑙−, and 𝑁𝑂3−)
together with the maximum possible concentrations of minor ions and heavy metals (𝐹𝑒2+, 𝑀𝑛2+, 𝐶𝑑2+, 𝐶𝑢2+,
𝐴𝑙3+, 𝑃𝑑2+ and 𝑍𝑛2+) based on pH, alkalinity and temperature. The model (II) was developed and tested to simulate pH and alkalinity in the near field, mixing zone considering only the effect of carbonaceous alkalinity.
Finally, the model (II) was extended to include the effect of iron (III) in the near field and a modelling methodology is proposed for simulating pH and alkalinity in the far field. The modelling methodology proposed is based on already demonstrated valid principles and the models results while not tested using laboratory or field data are as expected. The modelling methodology can be used for simulating processes in streams. For real cases calibration will be necessary by adjusting parameters such as the dispersion and mass transfer coefficients.
Key words: Water Quality, Monitoring systems, Modelling, pH and alkalinity
Supplementary bibliographical information Language: English
ISSN and key title: 1101-9824 ISBN (print) 978-91-7753-250-7
ISBN (pdf) 978-91-7753-251-4 Recipient’s notes Number of pages
Security classification
I, the undersigned, being the copyright owner of the abstract of the above-mentioned dissertation, hereby grant to all reference sources permission to publish and disseminate the abstract of the above-mentioned dissertation.
Signature Date 2017-04-27
VI
Sustainable Water Quality
Monitoring for Developing Countries
in the Context of Mining
Monitoring systems and modelling
Clemêncio M. Carlos Nhantumbo
VII
Cover photo by Jaime Palalane
Copyright Clemêncio Nhantumbo
Faculty of Engineering, Department of Building & Environmental Technology
Division of Water Resources Engineering
ISBN (print) 978-91-7753-250-7
ISBN (pdf) 978-91-7753-251-4
ISSN 1101-9824
REPORT 1070
Printed in Sweden by Media-Tryck, Lund University
Lund 2016
i
Dedication
I dedicate my thesis to my children Carla, Clemêncio and Kyara.
In your weakness you have possibilities, use them wisely!
ii
Acknowledgement
I thank my main supervisor Rolf Larsson for patient and close assistance for both
academic and social issues during my studies. I am grateful to my co-supervisors,
Magnus Larson and Dinis Juízo for encouraging and assisting me during my studies.
I express great respect to Kenneth M Persson for encouraging and supporting me
with chemistry in my work. I extend my gratitude to the assistance given by head of
division Hans Hanson and the administrative personnel.
I acknowledge the support by the Swedish International Development Agency
(SIDA) under the agreement EMU-SIDA 2011–2015 and a monthly stipend given
by the Lars Erik Lundberg Scholarship Foundation that allowed me to prolongate
my staying in Sweden during the last two years of my studies. I also thank Carlos
Lucas the Head of Cooperation Department and Nelson Matsinhe, the coordinator
of Integrated Water Resources Management under the agreement EMU-SIDA 2011-
2015 at Eduardo Mondlane University (EMU) for their patient assistance.
I thank my parents Ana and Carlos for giving me life and basic education that
allowed me to accept challenges in life and wisdom to turn them into achievements.
I thank my wife, Carla for giving me the reason to do everything in my life, my
children Kyara, Carla and Clemêncio Júnior. I thank my colleagues and all people
that supported me with my work and social life during my doctoral studies. Finally,
I express my gratitude to creator of life, I was taught to call him God, for giving me
opportunity to be part of his amazing creation.
iii
Popular summary
Mining is a source of revenue and it is now common in most developing
countries. However, it might cause severe impacts to the environment and most of
them are irreversible. Mining usually affects the rivers, lagoons and aquifers making
its water inappropriate for human activities and living species. In some cases, the
impacts of mining to the water resources come along time after the mining has
ceased. When mining has ceased, the mining areas often become completely
inappropriate for all kinds of live. Reclamation of areas impacted by mining is
expensive and it takes a long time to get satisfactory results. The way mining is
being done in developing countries, no money will be left to manage environmental
problems after mining closure which makes the situation even worse.
In Mozambique, mining is developing fast since 2010. Huge reserves of coal were
recently discovered in Tete province in the riparian areas of Zambezi River Basin.
The Zambezi River Basin is the largest river basin in Southern Africa with rich and
diversified environment and high potential for development of human activities
such as agriculture, navigation, hydropower production and recreation. Mining
threatens the environment in the riparian area of the river and the water quality is
one of the major issues.
To allow actions protection of water resources, water quality monitoring
programs are essential for understand the water quality changes while they are not
well established in most developing countries. There are water quality monitoring
systems developed and implemented successfully mostly in developed countries.
Lack of skilled people and financial resources limits the implementation of water
quality monitoring programs in developing countries. Improved water quality
monitoring system that considers the lack of resources is necessary for developing
countries in the context of mining development.
In this thesis, a water quality monitoring system, that takes into consideration the
lack of skilled people and financial resources that can be used for developed
countries in the context of mining development is proposed for Zambezi River Basin
in Mozambique. The system values the outcomes and goals of the government
aiming to guarantee financial support and the generation of good water quality
information. The system considers first to improve data sharing within the entities
doing water quality monitoring in the river basin and slowly move to a centralized
approach, where one company does the water quality monitoring for the entire river
basin. The centralized system will ensure consistence and comparability of the water
quality data, while reducing the overall monitoring cost. However, it is expected to
iv
be a challenge to convince all stakeholders, especially the coal mines to have the
same company doing monitoring.
Models are proposed to be used for reducing the cost of water quality monitoring
programs; either by (1) reducing the cost of sampling and analysis by estimating
difficult and costly to measure parameters using others that are easy to measure at
low cost; and (2) allocating the resources in areas where there is high risk of
pollution identified by simulating acidification and reclamation of streams already
impacted by acidic discharge. The last point is important for developing countries
because the resources are limited.
v
Abstract
Mining, seen as a source of revenue in most developing countries, threatens
seriously the environment. Mining impacts the water quality and one of the main
problems of mining is acid mine drainage. Low pH and high concentration of heavy
metals characterize acid mine drainage. When a stream is impacted by acid mine
drainage both human activities and the ecological system are seriously affected.
In Mozambique coal mining is growing faster since 2010 while water quality
monitoring programs are not well established and improvements are limited due to
lack of skilled people and financial resources. The major coal reserves of
Mozambique are located in the riparian area of Zambezi River Basin which is the
largest river basin in Southern Africa with 11% of its catchment area in
Mozambique. The Zambezi river basin in Mozambique has a high potential for
development of human activities and its environment is rich and diversified.
There are water quality monitoring systems already developed and successfully
implemented in developed countries. However, these systems are not sustainable
for developing countries due to lack of resources. A water quality monitoring system
that (1) produces consistent and comparable water quality information; (2) provides
feedback to outcomes and goals of the government; and (3) promotes continuous
improvement of the water quality, in the context of mining development and under
the constraint of lack of human and financial resources, is proposed for the Zambezi
River Basin in Mozambique. The system includes two alternative monitoring
procedures. It is concluded that the best way forward is to implement the first
procedure which improves the current situation by using web-based data sharing
and slowly move to the second procedure which is centralized and with one
company doing water quality monitoring for the entire river basin in Mozambique.
Modelling is an alternative solution for reducing the cost of monitoring by: (1)
estimating difficult and costly to measure parameters based on others which are
easily obtained and (2) simulating contamination and reclamation of already
impacted streams thus shifting usage of resources to monitor water quality changes
in more vulnerable areas. Existing surface water quality models have limitations in
simulating contamination of streams by acidic discharges. OTIS and PHREEQ C
are used for simulating mixing and transport of non-conservative pollutants but they
fail when the task is to simulate pH in streams which are influenced by equilibrium
reactions between the alkalinity species interacting with the surrounding
environment.
vi
Within the scope of this work two models were developed, model (I) for
estimating the concentration of inorganic ions in surface water, and model (II) for
simulating pH and alkalinity in streams impacted by acidic discharges. The model
(I) estimates the concentration of major ions (𝑁𝑎+, 𝐾+, 𝑀𝑔2+, 𝐶𝑎2+,𝐻𝐶𝑂3−, 𝑆𝑂4
2−,
𝐶𝑙−, and 𝑁𝑂3−) together with the maximum possible concentrations of minor ions
and heavy metals (𝐹𝑒2+, 𝑀𝑛2+, 𝐶𝑑2+, 𝐶𝑢2+, 𝐴𝑙3+, 𝑃𝑑2+ and 𝑍𝑛2+) based on pH,
alkalinity and temperature. The model (II) was developed and tested to simulate pH
and alkalinity in the near field, mixing zone considering only the effect of
carbonaceous alkalinity.
Finally, the model (II) was extended to include the effect of iron (III) in the near
field and a modelling methodology is proposed for simulating pH and alkalinity in
the far field. The modelling methodology proposed is based on already
demonstrated valid principles and the models results while not tested using
laboratory or field data are as expected. The modelling methodology can be used
for simulating processes in streams. For real cases calibration will be necessary by
adjusting parameters such as the dispersion and mass transfer coefficients.
vii
Papers
Appended papers
I. Nhantumbo, C., Larsson, R., Juizo, D. & Larson, M., 2015. Key issues for
water quality monitoring in the Zambezi River Basin in Mozambique in the
context of mining development. Journal of Water Resources and Protection
– [published]; DOI: 10.4236/jwarp.2015.75035
II. Nhantumbo, C., Larsson, R., Larson, M., Juizo, D. & Persson, K., 2015. A
simplified model to estimate the concentration of inorganic ions and heavy
metals in rivers. Water Journal – [published]. DOI 10.3390/w8100453;
III. Nhantumbo, C., Carvalho, F., Uvo, C., Larson, M., & Larsson, R., 2017.
Applicability of a processes-based model and artificial neural networks to
estimate the concentration of major ions in rivers. Journal of Geochemical
Exploration [submitted];
IV. Nhantumbo, C., Larsson, R., Larson, M., Juizo, D. & Persson, K., 2017.
Simplified model to simulate pH and alkalinity in the mixing zone of surface
water and acidic discharge (pH-mixing model). Mine Water and
Environment – Submitted [under-review]
V. Nhantumbo, C., Larsson, R., Larson, M., Juizo, D. & Persson, K., 2017.
Modelling pH and alkalinity in streams impacted by acidic discharges.
Journal of Hydrology [submitted].
Author’s contribution to appended papers
I. The author did the literature review, study visits to Zambezi River Basin,
mining companies and government organization in Mozambique to collect
information about mining activity and water quality monitoring in Zambezi
River Basin. The author conducted two seminars together with co-authors
in Maputo and Tete in Mozambique to discuss the water quality monitoring
system and procedures proposed with relevant stakeholders. The author
wrote the first version of the paper and participated in editing of the paper.
viii
II. The author developed the model and wrote the first draft of the paper with
technical support of the co-authors. The author also participated in editing
of the paper.
III. The author did the comparative analysis of the physical processes based
model and the artificial neural networks model and wrote the first draft of
the paper. Co-authors supported in analysing data and editing of the paper.
IV. The author with support of the co-authors developed the model and did
laboratory experiments to generate data to test the model and wrote the first
draft of the paper. The author also worked together with the co-authors in
editing of the paper.
V. The author developed the model, did the analysis of the results, and wrote
the first draft of the paper with support of the co-authors. The author also
worked with editing of the paper.
Other publications
I. Nhantumbo, C., Larsson, R., Larson, M., Juizo, D. & Persson, K.,
2015.Applicability of water quality monitoring systems and models in
developing countries in the context of mining development. 5th
International Conference on Environmental Science and Development.
[published]. DOI: IJMAS-IRAJ-DOI-3873.
II. Nhantumbo, C., Larsson, R., Larson, M., Juizo, D. & Persson, K.,
Modelling pH and alkalinity in rivers impacted by acid mine drainage.
IMWA conference 2016 – [published].
https://www.imwa.info/docs/imwa_2016/IMWA2016_Nhantumbo_167.p
df;
ix
Content
1. Introduction ....................................................................................................1
1.1 Background ...........................................................................................1
1.2 Objectives .............................................................................................2
1.3 Methods ................................................................................................2
1.4 Limitations ............................................................................................3
2. Study area .......................................................................................................4
2.1 Zambezi River Basin ............................................................................4
2.2 Coal mining ..........................................................................................5
2.3 Water Quality Monitoring in Zambezi River Basin .............................7
3. Water Quality Monitoring Systems ................................................................8
3.1 Review of water quality monitoring systems .......................................8
3.2 Water Quality Monitoring System for Zambezi River Basin .............11
4. Use of Models for Water Quality Monitoring ..............................................16
4.1 Theory .................................................................................................18
4.2 Model 1- Estimating inorganic ions in surface water .........................25 4.2.1 Modelling methodology .........................................................25 4.2.2 Evaluation of performance of model 1 ...................................27 4.2.3 Results and discussion ............................................................28 4.2.4 Comparing the model with Artificial Neural Networks .........29
4.3 Model 2 - pH and alkalinity in streams ..............................................32 4.3.1 Simulating pH and alkalinity in the mixing zone ...................33 4.3.2 Methodology for simulating pH and alkalinity in streams .....41
4.4 Applicability and limitations of the models ........................................56
5. Conclusions and recommendations ..............................................................59
6. Future work ..................................................................................................61
References ..............................................................................................................62
x
1
1.Introduction
1.1 Background
Mining has been impacting the water quality of rivers worldwide. Cases of mining
impacting water resources have been reported in several countries such as USA,
Brazil, Australia, Spain, South Africa, and China (Anawar, 2015; DPLF, 2014;
ICMM, 2012; Ochieng, Seanego, & Nkwonta, 2010). The main issue of mining
impacting water resources is acid mine drainage (AMD) (Anawar, 2015; Ochieng,
Seanego, & Nkwonta, 2010). The impact of AMD to the environment can be over a
long period such as for Rio Tinto in Spain or severe as the Iron Mountain in
California (Olías & Nieto, 2015; Nordstrom, Alpers, Ptacek, & Blowes, 2000) .
Water quality monitoring is essential, when water is impacted or at risk of being
impacted, for allowing adoption of management solutions to protect the
environment before severe damages occur.
Mining is now common in most developing countries while water quality
monitoring programs are not well established (Paper I). In Mozambique coal
production was expected to grow from about 0.036 million tons in 2010 to 20
million tons in 2015 (Paper I). The largest coal mining area in Mozambique is
located in Zambezi River Basin which is the largest river basin in Southern Africa
and has about 11% of its total area in Mozambique (Paper I). Monitoring programs
in developing countries are limited regarding the number of parameters monitored
and the volume of samples analyzed. Although efforts are made, lack of human and
financial resources limit improvements (Paper I). Poor legislation is also limiting
water quality monitoring in developing countries (Pondja, Persson, & Matsinhe,
2016).
A water quality monitoring system improved and supported by models are an
alternative solution (Paper I, Paper II). Water quality monitoring systems and
models are used mostly in developed countries. The most well-known water quality
monitoring systems are (1) Result-Based Monitoring and Evaluation, (2)
Framework for Water Quality Monitoring, and (3) Monitoring System adopted by
the European Union (EU) under EU Water Framework Directive (Paper I).
However, these systems were not developed to be used for cases where there is
mining development with limited resources to do water quality monitoring (Paper
2
I). There are also models that can be used to support water quality monitoring such
as Streeter–Phelps, the QUAL, WASP, QUASAR, MIKE, BASIN, EFDC, and
PHREEQ C (Wang, Li, Jia, Qi, & Ding, 2013). However, none of these models were
developed specifically to deal with water quality evolution in rivers affected by
mining. The models also require a lot of input data to perform simulations, while
such data are not readily available in most developing countries (Paper II).
1.2 Objectives
The main objective of this thesis is to suggest improved water quality monitoring
system supported by models. The system is to be used for monitoring water quality
in the context of mining in developing countries where human and financial
resources are limited.
To fulfil the main objective the following specific objectives were formulated:
• Review available water quality monitoring systems and suggest one for
Zambezi River Basin based on the existing conditions;
• Evaluate the applicability of available surface water quality models in the
context of mining development;
• Develop a model for reducing sampling and analysis, thus reducing the
cost of water quality monitoring programs;
• Develop a model for simulating contamination of streams due to acidic
discharge.
Although, improved water quality monitoring systems are of interest for most
developing countries. The Zambezi River Basin was selected as study area to make
the results of the study more specific. Still, data from Swedish rivers was used to
test the developed model due to lack of data in Zambezi River Basin and other rivers
in developing countries.
1.3 Methods
The thesis was based on literature reviews, site visits, laboratory experiments and
developing computer model algorithms using Python, Fortran and MATLAB.
Literature reviews conducted were focused on the available water quality
monitoring systems, and models that can be used in developing countries in the
context of mining development as well as for understanding the main problems of
mining and theories used for modelling. Site visits were conducted to (i) an area
already impacted by coal mining, Criciúma in Brazil, to understand the common
problems of mining as well as, (ii) to the coal mining area, Zambezi River Basin
3
and the institutions responsible for doing water quality monitoring in Mozambique,
to understand the main problems of water quality monitoring. Laboratory
experiments were performed to generate data to test the model for simulating pH
and alkalinity at the mixing zone. Finally, the models were converted into three
computer algorithms, (1) for estimating inorganic ions in water, (2) for simulating
pH and alkalinity in the near field mixing zone when acidic water is discharged into
a stream, and (3) for simulating pH and alkalinity downstream the mixing zone.
1.4 Limitations
Lack of data made it impossible to test the models for rivers in developing countries
where the models are expected to be used. Data from Swedish rivers was used to
test model 1, while laboratory data was used for testing model 2 for simulating pH
and alkalinity in the mixing zone. The model 2 which can be used to get a first
estimate of pH and alkalinity in the mixing zone still needs some improvement for
simulating contamination by acid mine drainage. An extension of the model to
include more alkalinity species is also necessary,
Model 2 is further extended to simulate pH and alkalinity in the near field mixing
zone by including iron as well as for simulating the process downstream of the
mixing zone. The model was developed based on already validated theories and
concepts. However, due to the complexity of the model and the limited time for
concluding this study it was not possible to gather data to test the extended model.
4
2.Study area
The riparian area of Zambezi River Basin in Tete province was selected as study
area. This area was selected because it has the largest coal reserves of Mozambique
and coal mining is developing faster since 2010 while a water quality monitoring
program is not well stablished. The region has rich biodiversity and has high
potential for development of human activities such as agriculture and hydropower
production. An improved water quality monitoring program that allows
understanding of water quality changes is necessary for sustainable management of
water resources.
2.1 Zambezi River Basin
The Zambezi River Basin (ZRB) is the largest river basin in Southern Africa with
about 1 370 000 km2 and average discharge at the outlet of 4100 m3/s (World Bank,
2009). Eleven percent (11%) of total area of ZRB is in Mozambique. ZRB sustains
life of about 30 million people and keeps the natural environment rich and
diversified. The river is essential for the economy of its riparian countries which
include Angola, Botswana, Malawi, Mozambique, Namibia, Tanzania, Zambia, and
Zimbabwe, see Figure 1 (World Bank, 2009).
The average precipitation in ZRB is 950 mm/year. Due to uneven rainfall
distribution, the north part of the river basin contributes with more runoff compared
to the south part. The highest precipitation, about 2400 mm/year has been observed
in the northeast part of the basin, and the lowest, about 500 mm/year in the southeast
part. The main stream of ZRB crosses the Mozambican border with an average flow
of about 2300 m3/s. On its way through Mozambique it receives another 1800 m3/s,
about 70% out of which comes from the mining area (Paper I).
Twelve dams and almost 53 new projects of dams were being analysed until 2008.
The total installed capacity for energy production in Zambezi River is
approximately 5000 MW. The largest hydroelectric power plant is Cahora-Bassa
dam (2075 MW), which is located in Tete province in Mozambique (World Bank,
2009). Zimbabwe had the largest irrigated area among the riparian countries with
108 717 ha compared to Mozambique, which only has 8 436 ha. However, studies
show that Mozambique has higher potential for irrigation compared to all other
5
riparian countries with about 600 000 ha (World Bank, 2009). Ninety percent (90%)
of urban and fifteen percent (15%) of rural domestic water supply in the ZRB is
from surface water, whereas the remaining water supply is from groundwater
sources (SADC-WD/Zambezi River Authority, 2007).
Figure 1 Zambezi River Basin (Paper I)
2.2 Coal mining
Coal mining in Mozambique started during the colonial period in 1920 by
Portuguese companies (Alexandre, 2012). The highest production before 2004,
about 575 000 tons/year was reached in 1981 (Alexandre, 2012). In 2004, the
Mozambican government launched an international contest for the development of
the Moatize Coal Reserve that was won by Companhia do Vale do Rio Doce
(Alexandre, 2012). In 2014 there were more than 60 licenses and 40 requests for
licenses for coal mining in Mozambique that are owned by around 30 companies,
Figure 2. There were three companies extracting coal at the end of 2011, all of
which were located in Moatize. Until 2012 seven companies were extracting coal in
6
Tete: Vale Moçambique, Rio tinto, Minas de Moatize, Jindal in Changara district,
ENRC, Ncondedzi Coal Company, and Minas Revúbue (Paper I).
Figure 2 Coal mining in Zambezi River Basin in Mozambique (paper I)
The ministry of Mineral Resources (MIREM) has produced projections of coal
production in Mozambique that show a growth of coal production from 2.9 million
of tons in 2011 to 39.0 million of tons in 2019. After this peak the production would
reduce to 6.7 million of tons until 2028. However, coal production in Mozambique
reduced already in 2015 due to lowering of prices of coking coal in the international
market. The coking coal cost was less than 100 USD per tonne after 2015. However,
since November 2016 the price of coking coal in the international market rose to
260-270 USD/tonne, and as a result the coal production in Mozambique is
increasing again (Scala, 2017).
7
2.3 Water Quality Monitoring in Zambezi River Basin
A river basin organization, Zambezi Watershed Commission (ZAMCOM) was
created in 1995 and came into force in 1998. The organization was created to
promote equitable and reasonable utilization of the water resources of the Zambezi
watershed as well as efficient sustainable management for the river basin.
Unfortunately, lack of resources and low data availability limit the implementation
of sustainable, integrated water resources management.
ARA – Zambeze is the regional administration of water responsible for the
management of Zambezi River Basin in Mozambique (Paper I). Three types of
monitoring are done in the Zambezi River Basin: Surveillance, Operational, and
Investigative Monitoring. Surveillance Monitoring is done by ARA-Zambeze, and
includes only the basic parameters: temperature, pH, electric conductivity, total
dissolved solids, dissolved oxygen, orto redox phosphate, salinity, turbidity, color,
smell, chlorates, total coliforms, and fecal coliforms (ARA-Zambeze, 2012).
Operational monitoring is done by the companies using and/or affecting the water
of the river. Finally, investigative monitoring is performed by the Institute of Fish
Investigation of Songo and other research institutions (Paper I). However, the lack
of resources limits the water quality monitoring performed in ZRB. Thereby is not
allowing understanding of water quality changes to protect the water resources
(Paper I). Understanding water quality changes gets even more important due to
mining development within the river basin in Mozambique.
Industries including mining companies, that could impact the environment during
their activities have obligation under Mozambican legislation of doing
environmental impacts assessment and submit the reports to the Ministry of Land,
Environment, and Rural Development before starting their activities. Additionally,
industries which have high probability of impacting water resources have obligation
of doing water quality monitoring in their area of influence and submit periodical
physical reports to the river basin organization. For the case of coal mines with their
activities based in the riparian area of Zambezi River Basin in Mozambique, the
reports are submitted to ARA-Zambeze. However, the capability of ARA-Zambeze
in doing operative oversight for the water quality monitoring done by the mining
companies is limited and there is no way of making sure that the water quality
monitoring information in the submitted reports is accurate.
8
3.Water Quality Monitoring Systems
As stated before, a water quality monitoring system for the Zambezi River Basin
that takes into consideration the lack of human and financial resources in the context
of mining development is to be proposed. The system should be based on available
water quality monitoring systems and the actual conditions in Zambezi River Basin
as described in chapter 2.
3.1 Review of water quality monitoring systems
A variety of water quality monitoring systems have been developed. As
mentioned in the introduction, the most well-known systems are (1) Result-Based
Monitoring and Evaluation, (2) Framework for Water Quality Monitoring, and (3)
Monitoring System adopted by the European Union (EU) under the EU Water
Framework Directive. These systems have differences and similarities depending
on the objective for which they were developed.
i) Result-Based Monitoring and Evaluation (World Bank)
The World Bank has adopted the Result-Based Monitoring and Evaluation
System (RMES) for integrated water resources management (IWRM Plan Joint
Venture Namibia, 2010). RMES is an improved version of Implementation-Focused
Monitoring and Evaluation, designed to address the “did they do it?” question. The
main weakness of the Implementation-Focus Monitoring and Evaluation is that it
does not provide the policymakers with information on success or failure of the
project, program, or policy (Kusek & Rist, 2004).
RMES was designed to answer the “so what?” question, which it does by
providing feedback on actual outcomes related to the goals of the government
(Kusek & Rist, 2004). The system also checks if the water quality is being protected
with implemented actions. The system scheme is presented as a table and has 10
steps, see figure 3.
9
Figure 3 Ten Steps for building a result-based monitoring and evaluation system (RMES) adapted from: (Kusek & Rist, 2004) and (IWRM Plan Joint Venture Namibia, 2010) (Paper I)
Although monitoring objectives are not explicitly defined, RMES includes three
issues which are not considered in the other monitoring systems: 1) selecting the
key indicators that determine the willingness of the different stakeholders to
cooperate with the monitoring; 2) defining the monitoring outcomes; and 3)
sustaining the system within the government. This system was designed to ensure
that the government goals are satisfied intending to guarantee support for the
monitoring program.
The Ministry of Agriculture, Water and Forest of Namibia proposed the use of
RMES during the implementation of Integrated Water Resources Management
(IWRM) (IWRM Plan Joint Venture Namibia, 2010). In the context of
implementing IWRM the Namibian government discussed a funding allocation
procedure for involving all water users. This brings up the fourth principle of the
Dublin Statements which considers water as an economic good and states that the
users should pay for the use of water to guarantee availability, management, and
conservation of the resource. This system was also implemented in some developed
countries, such as Australia, Canada, Netherlands, and United States (Kusek & Rist,
2004).
1
2
3
4
5
6
7
8
9
10
Ten Steps to Building a Performance Based M&E System
Conducting a Readiness Assessment – To determine the capacity and willingness of the governments and partners to implement
the M&E System. Identifying barriers, who will own, protectors and resisters to the implementation of M&E System
Agreeing on Outcomes to Monitor and Evaluate – The outcomes should derive from the strategic goals of the country .
They should be focused and drive the capability to allocate resources and activities of the government and its partners.
Developing Key Indicators to Monitor Outcomes – It is the mean of assessing if the outcomes are being achieved.
Developing appropriate key indicators is crucial for M&E process, it influences data collection, analysis and reporting.
Gathering Baseline data on Indicators –means essentially to take the first measurement‘s of the indicators or it can be
viewed as the measurement of the initial conditions of the indicators toward the outcomes.
Planning for Improvements /Setting Realistic Targets – It is important to recognize that most of the outcomes are long-term,
complex, and not easily achieved. Thus there is need to specify mid-term targets that specify the progress toward the outcomes.
Monitoring for Results – It is administrative and institutional task of establishing data collection, analysis, and reporting
guidelines.
Evaluative Information to Support Decision - making – Focus on the contributions that evaluations studies and analysis can
make throughout the process of evaluating the results and movement toward the outcomes.
Analyzing and Reporting the Findings – It determines what findings are reported to whom, in what format and which intervals.
It is a crucial step to produce information for M&E System.
Using Findings – The process should not generate information only but it is important that the information reach the appropriate
users in the system in reasonable time in order to be used to take decisions .
Sustaining the M&E System Within the Government – There are six criteria which have to be considered when constructing a
sustainable system: demand, structure, trustworthy and credibility of information, accountability, incentives and capacity.
10
ii) Framework for Water Quality Monitoring (US-NWQMC)
The Framework for Water Quality Monitoring (FWQM) was developed and
implemented in the USA. This system was developed to enhance production of
consistent and comparable water quality information by (1) analyzing the
characteristics and trends of water quality; (2) identifying emerging water quality
issues; and (3) checking the compliance with regulations to support fair and
equitable water resources management (AWRA, 2004; Peter & Ward, 2004). A
graphical representation of FWQM was proposed by the National Water Quality
Monitoring Council (NWQMC), see Figure 4a.
Figure 4 a) Framework for water quality monitoring (FWQM) adapted from NWQMC (AWRA, 2004). b) River Basin Management Planning Cycle adopted by European Union through EU-WFD. (adapted from Paper I)
The system has a cyclic approach with six elements, Figure 4a: 1) develop
monitoring objectives; 2) design monitoring program; 3) collect field and laboratory
data; 4) compile and manage data; 5) assess and interpret data; and 6) convey results
and findings. Additionally, four issues must be considered when implementing the
FWQM: identify data users; engage monitoring partners; evaluate the monitoring
program; and use information technology to connect the framework elements (Peter
& Ward, 2004). The system also values communication, collaboration and
cooperation as means for meeting the monitoring objectives which are typically
defined to answer the following questions: (1) Is the water acceptable as potable
water or for swimming and other aquatic uses or habits?; (2) Is the water quality
getting better or worse?; (3) Is the water quality changing due to certain water uses
or management?; (4) Are the water quality requirements being met? and (5) How
Develop
Monitoring
Objectives
Design
Monitoring
Program
Collect
Field and
Lab Data
Convey
Results and
Findings
Assess and
Interpret
Data
Compile and
Manage Data
Understand
Protect
restore
Setting/Reviewing
of Quality
Standards
Characte-
rization
Classifi
-cation
Monitoring
a) b)
11
does the water quality of a certain water body compare with other water bodies?
(AWRA, 2004; Spooner & Mallard, 2004).
iii) Water Resources Monitoring System Adopted under the EU Water
Framework Directive
The European Union through the European Union Water Framework Directive
(EU-WFD) adopted the River Basin Management Planning Cycle, Figure 4b. This
cycle includes two cycles presented in the inner and outer rings of a circle. The outer
ring describes the process which has to be followed for implementing management
options and the inner ring describes continuous investigation of water quality
changes. The outer ring has three steps for implementing management options:1)
Develop and Publish the River Basin Plans; 2) Implement Measures in Management
plans; and 3) Review Effectiveness of Management Plans. The inner ring has three
steps as well: 1) Setting/Reviewing of Quality Standards; 2) Characterization;
Monitoring; and 3) Classification. The inner ring aims to guarantee that the water
quality changes are understood and the outer ring aims to guarantee that the
management options are continuously being implemented and improved based on
the results of previously implemented management options and water quality
changes obtained from water quality monitoring.
The EU-WFD distinguishes three types of water quality monitoring programs:
surveillance, operational and investigative monitoring. Surveillance monitoring
gives the overall water quality status within the catchment. Operational monitoring
is required where pollution or other types of impacts on ecological status is apparent.
Investigative monitoring is required when the surveillance monitoring shows that
the objectives are not being met and when the operational monitoring is not yet
established.
3.2 Water Quality Monitoring System for Zambezi
River Basin
Water quality monitoring systems have been implemented successfully in
developed countries. The main reason for failure of water quality monitoring
programs in developing countries is lack of skilled people and financial resources.
In developing countries, few activities are fully funded compared to the ones that
are proposed or necessary. Immediate education and health problems such as
reducing the level of illiteracy as well as fighting epidemic diseases have priority
compered to water quality monitoring. Thus, it is important to show that water
quality monitoring is a key issue to guarantee continuous access to basic needs such
12
as potable water and productive agricultural land. Focusing on the government goals
and outcomes is a key issue for getting support for water quality monitoring
programs as suggested in RMES. However, it is important to have a system that
guarantees production of consistent and comparable water quality data as well as
continuous improvement of the system using a cyclic view as the FWQM and EU-
WFD.
A system that combines the principles of FWQM, RMES and EU-WFD is
proposed for ZRB, Figure 5 (Paper I). The system is proposed to produce consistent
and comparable water quality information; providing feedback to outcomes and
goals of the government; while guaranteeing continuous improvement of the
system, in the context of mining development and under the constraint of lack of
human and financial resources. The system has two levels, the higher level and the
operational level. At higher level the monitoring system starts by reviewing the
government goals as defined by national legislation and ends reviewing if the
government goals and outcomes are satisfied. At operational level the monitoring
system starts by selecting the target pollution sources to guarantee that more
resources are used where the likelihood of having water contamination is higher and
ends by using the findings for defining water protection measures.
Two alternative water quality monitoring procedures are proposed to
operationalize the monitoring system where each stakeholder has its duty clearly
defined, Figure 6 and 7 (Paper I). The first monitoring procedure is based on an
improved data sharing system, where companies doing water quality monitoring for
different reasons in the river basin as well as the government organizations have a
common web-based water quality database. The water quality database should allow
for doing overall water quality change analyses in the river basin as well as water
quality trend analyses. The second water quality monitoring procedure, is based on
having one single consulting company responsible for doing water quality
monitoring for the entire river basin. The companies, and the government
organizations should pay the company for water quality monitoring according to
their interests. The latter procedure has advantages compared to the first procedure
such as: (1) making sure that all water samples are analyzed using the same methods
allowing comparability and more accurate trend analysis; (2) reducing the water
quality monitoring cost by reducing the number of samples analyzed by the same
equipment. However, the second procedure has challenges, such as: (1) convincing
all stakeholders to accept having the same company doing water quality monitoring
in their area of influence; (2) ARA-Zambeze has to guarantee that the consulting
company is producing good water quality monitoring data by doing operational
oversighting.
13
Figure 5 Water quality monitoring system proposed for Zambezi River Basin (Paper I)
Government Politics/Objectives
National Water Policy published in August 1991 Chapter IV ( Water Quality Protection)
Evaluation of the Outcomes/ Are the Government Objectives being meet?
Conduct the readiness assessment
Defining the monitoring objectives
Select indicators
Selecting the target pollution source Coal Mining. Note: Important to consider the other pollution sources
Water legislation available which forces all stakeholder to cooperate
Evaluate the impact of coal mining and other activities to the water of Zambezi River Basin
pH, temperature and concentrations of sulfate, iron, magnesium, alkalinity and changes in fish
population. Note: other parameters may be included if seems relevant and it is important to use models
to predict other parameters whenever is possible from the monitored parameters before any other
analysis to minimize the costs.
Gathering a baseline data
Design monitoring program
Monitoring for results
There is lack of historical data about the water quality of Zambezi River in Mozambique, but based on
the information obtained the water quality of the river is not strongly impacted. There are other impacts
due to Cahora-Bassa dam, but the pH was not affected. Note: This may be improved after obtaining the
first set of monitoring data.
Two different approaches are proposed to monitor the water quality of Zambezi River Basin in
Mozambique. In both cases its taken into account the lack of resources and ARA-Zambeze acts as a
coordinator. In the first approach of water quality is monitored by the different stakeholders and reported
to ARA-Zambeze. In the second approach the water quality of entire river basin is monitored by a
consultancy company. Note: See the development of this in the text and figure 5 and 6.
Collecting data, sampling, laboratory analysis, technical reports of results, quality assurance and quality
control.
Evaluation of the information Comparing with standards and analyzing trend analysis.
Reporting findings and suggestionsBased on the evaluation the findings are reported, mitigation measures and emergency actions are
suggested. The target audience for these reports are the water users and policy-makers.
Using the findings
The mitigation measures are discussed in general meeting with different stakeholders organized by
ARA-Zambeze. The final decision about the implementation of the measures is taken by ARA-Zambeze.
The emergency action can be implemented without previous discussion in the general meetings but it is
important to inform the stakeholders affected by the actions before.
14
Figure 6 First suggested procedure for water quality monitoring for Zambezi River Basin. Improved data sharing system (Paper I).
Figure 7 Second suggested procedure for water quality monitoring for Zambezi River Basin. All monitoring performed by one consulting company (Paper I)
IIP- Songo
• Monitor fish in vulnerable
areas;
• Prepare reports of fish
monitoring;
• Suggest mitigation measures;
• Participate in meetings.
Coal mining companies
• Do operative monitoring;
• Suggest mitigation measures;
• Finance mitigation measures;
• Prepare reports to ARA-
Zambeze
• Participate in meetings.
Industries and others related
• Do operative monitoring;
• Prepare reports to ARA-
Zambeze
• Suggest mitigation measures;
• Finance mitigation measures;
• Participate in meetings.
Domestic water supply
companies and others related
• Prepare reports to ARA-
Zambeze
• Suggest mitigation measures;
• Participate in meetings.
Environment
People
Resources Time
ARA-Zambeze
• Do surveillance monitoring;
• Prepare reporting forms;
• Do the operative oversight;
• Prepare general monitoring reports;
• Suggest mitigation measures;
• Implement mitigation measures;
• Implement emergency actions
• Schedule annual meetings.
Consulting company
• Monitor water quality
• Prepare the reports of water quality
IIP- Songo
• Monitor fish in vulnerable areas;
• Prepare reports of fish monitoring;
• Suggest mitigation measures;
• Participate in meetings.
Coal mining companies
• Finance mitigation measures;
• Suggest mitigation measures;
• Participate in meetings.
Industries and others related
• Finance mitigation measures;
• Suggest mitigation measures;
• Participate in meetings.
Domestic water supply
companies and others related
• Suggest mitigation measures;
• Participate in meetings.
Environment
People
Resources Time
ARA-Zambeze
• Do the operative oversight;
• Implement mitigation measures;
• Implement emergency actions
• Schedule annual meetings.
15
As mentioned before the water quality monitoring system is proposed aiming to
guarantee that the government goals and outcomes are satisfied; the water quality
information generated is consistent and comparable; and the system still yields
satisfactory water quality data even though there is a lack of resources. The higher
level aims to guarantee that the government goals are satisfied, thus ensuring
continuous support for the water quality monitoring system. The operational level
aims to guarantee generation of consistent and comparable water quality data with
continuous improvement of the water quality monitoring system. Finally, the
proposed procedures aim to generate sufficient water quality information even
though there is a lack of resources, through efficient data sharing within the
stakeholders (first procedure, figure 6) and centralizing the water quality monitoring
(second procedure, figure 7). The other tool which is expected to be used for
reducing the water quality monitoring cost are models, discussed in chapter 4.
16
4. Use of Models for Water Quality
Monitoring
Models can be used together with improved water quality monitoring systems for
reducing the need for skilled people and financial resources. Models can be used
for: (1) estimating water quality parameters based on the ones that are easy to
measure, thus reducing the cost of sampling and analysis needed for water quality
monitoring (Paper II); and (2) simulating different scenarios of pollution allowing
for properly planning of water quality monitoring and reclamation of impacted
streams (Paper IV). Simulating contamination of streams due to available sources
of pollution as well as simulating reclamation of streams allows allocating resources
in areas with high risk of pollution. Proper allocation of resources is important
particularly when they are limited.
Mining activity typically impacts water quality by: (1) increasing turbidity and total
solids concentration; (2) lowering pH, thus affecting the solubility of minerals in the
stream bed and increasing the concentration of heavy metals, known as acid mine
drainage (AMD); and (3) causing precipitation of minerals such as iron hydroxide
that coat the stream bed (Paper II). AMD is one of the major issues of mining.
Monitoring and understanding pH changes in water is crucial when there is mining
(Paper II). Thus, it is important (1) to have models that can simulate pH change in
streams impacted by acidic discharge; and (2) to have a model that estimate other
parameters based on pH to be used in streams impacted by acidic discharges since
pH influence several water quality parameters.
Surface water quality models such as Streeter-Phelps, QUAL, WASP, QUASAR,
MIKE, BASIN Model, EFDC, OTIS and PHREEQ C can be used for simulating
processes in streams (Walton-Day, Paschke, Runkel, & Kimball, 2007; Wang, Li,
Jia, Qi, & Ding, 2013). Some of these models cannot simulate pH such as the
Streeter-Phelps model which was developed to simulate oxygen balance as a first
order biological oxygen demand decay (Rinaldi & Soncini-Sessa, 1977). While
models such as OTIS and PHREEQ C can be used to simulate mixing and transport
of non-conservative pollutants (Parkhurst & Appelo, 2013; Walton-Day, Paschke,
Runkel, & Kimball, 2007), PHREEQ C is also used to simulate speciation of water,
estimating concentration of soluble ions based on mineralogy (Parkhurst & Appelo,
2013).
17
When using PHREEQ C for simulating either speciation or mixing in streams it is
assumed that there is equilibrium of water with stream bed minerals such as calcite
(𝐶𝑎𝐶𝑂3 ), dolomite (𝐶𝑎𝑀𝑔(𝐶𝑂3)2) and/or gypsum (𝐶𝑎𝑆𝑂4 ∙ 2𝐻2𝑂) as well as with
𝐶𝑂2 in the atmosphere (Parkhurst & Appelo, 2013). When acidic water is
discharged into a stream the equilibrium of alkalinity species ( 𝐻+, 𝑂𝐻−, 𝐶𝑂32−,
𝐻𝐶𝑂3−, and 𝐻2𝐶𝑂3) within the water column is reached in shorter time compared to
the time necessary to reach equilibrium with stream bed minerals and 𝐶𝑂2 in the
atmosphere at the lower and upper boundaries respectively. Lower values of pH and
different concentrations of dissolved ions might characterize the mixing zone
compared to the one estimated using equilibrium with stream bed minerals and 𝐶𝑂2
in the atmosphere. When using OTIS to simulate mixing, only the dilution effect is
considered, while equilibrium between the alkalinity species cannot be simulated
(Walton-Day, Paschke, Runkel, & Kimball, 2007).
Two models are proposed, the first model (Model 1) to estimate the concentration
of major ions based on pH, alkalinity and temperature; and the second model (Model
2) to simulate pH and alkalinity in the mixing zone as well as the reactional transport
process downstream the mixing zone in streams impacted by acidic discharges,
Figure 8. The models can be used separately, but they can also be combined to get
a water quality model that simulates pH and alkalinity in streams impacted by acidic
discharges as well as getting speciation in terms of inorganic ions.
Figure 8 Modelling strategy. The model has two components, model 1 which estimates the concentration of major ions based on pH, alkalinity and temperature and model 2 which estimates pH and alkalinity in the near field, mixing zone and further downstream in the far field.
Modelling
Model
Simulates pH, alkalinity and
concentration of inorganic ions in
rivers
Model 1
Estimates concentration of inorganic ions
based on pH and alkalinity
Model 2
Simulates pH and Alkalinity in streams
impacted by acidic discharge
18
4.1 Theory
For the modelling, the following concepts and theories were used: carbonic acid
and iron hydroxide (III) dissociation, total alkalinity, protolithic theory of water;
major ions, solubility, conductivity, and mass flux. The main idea behind the
modelling is to combine existing theories and concepts to develop water quality
models that can be used for minimizing the water quality monitoring costs in
streams impacted by acidic discharges.
i) Carbonic acid equilibrium
Carbonate equilibrium defined by reactions equations 1, 1a, 2 and 2a relates pH
with concentration of carbonate alkalinity species in water. Equilibrium constants
can be estimated using temperature dependent correlations (Appelo & Postma,
1999).
332 HCOHCOH (1)
32
31
COH
HCOHKa
(1a)
2
33 COHHCO (2)
2
3
2
3
2HCO
COHK a
(2a)
The sum of concentration of all inorganic carbon species is called total inorganic
carbon (TIC). TIC is conservative with respect to mixing and is calculated using
equation 3.
2
3332 COHCOCOHTIC (3)
The concentration of each inorganic specie is calculated using equations (4)-
(6).The values of the constants, 𝛼𝐻2𝐶𝑂3, 𝛼𝐻𝐶𝑂3
−, and , 𝛼𝐶𝑂32− represent the
contribution of each carbonate specie to the TIC and the sum of their values is
therefore equal one.
TICCOH COH 32
][ 32 (4)
19
TICHCOHCO
3
][ 3 (5)
TICCOCO
23
][ 2
3 (6)
The constants 𝛼𝐻2𝐶𝑂3, 𝛼𝐻𝐶𝑂3
−, and, 𝛼𝐶𝑂32− are calculated as functions of the
concentration of hydrogen ions and equilibrium constants, equations (7)-(9). These
equations are obtained combining equations 1a, 2a, 3 and (4)-(6).
211
2
2
][][
][32
aaa
COHKKHKH
H
(7)
211
2
1
][][
][
3
aaa
a
HCO KKHKH
HK
(8)
211
2
21
][][23
aaa
aa
CO KKHKH
KK
(9)
ii) Iron hydroxide (III) equilibrium
Using the analogy with carbonic acid equilibrium, iron hydroxide (III)
equilibrium is described by equations (10)-(12). The equilibrium constants are
calculated using equations (10a)-(12a). The values of constants are available in the
literature for 25⁰C (Appelo & Postma, 1999).
OHOHFeOHFe 23 (10)
3
21
OHFe
OHOHFeK
(10a)
OHOHFeOHFe
2
2 (11)
2
2
2OHFe
OHOHFeK (11a)
OHFeOHFe 32
(12)
2
3
3OHFe
OHFeK (12a)
The sum of concentration of all iron species (III) is called total iron (III). Like
TIC, total iron (III) (TFe) is also conservative with respect to mixing. Total iron (III)
is calculated using equation 13.
20
32
23 FeOHFeOHFeOHFeTFe (13)
The concentration of each iron specie can be calculated using equations (14)-
(16).The values of constants, 𝛽Fe(𝑂𝐻)3, 𝛽𝐹𝑒(𝑂𝐻)2
+, 𝛽𝐹𝑒(𝑂𝐻)2+, and 𝛽𝐹𝑒3+ represent
the contribution of each iron (III) specie to the total iron (III) and the sum of their
values is therefore equal one.
TFeOHFe OHFe 33 (14)
TFeOHFeOHFe
22 (15)
TFeOHFeOHFe
2
2 (16)
TFeFeFe
3
3 (17)
The constants 𝛽Fe(𝑂𝐻)3, 𝛽𝐹𝑒(𝑂𝐻)2
+, 𝛽𝐹𝑒(𝑂𝐻)2+, and 𝛽𝐹𝑒3+ are calculated as a
function of concentration of hydroxide ions and equilibrium constants, equations
(18)-(21). This equations are obtained combining equations 10a, 11a, 12a, 13 and
(14)-(17).
32121
2
1
3
3
3
KKKOHKKOHKOH
OHOHFe
(18)
32121
2
1
3
2
1
2 KKKOHKKOHKOH
OHKOHFe
(19)
32121
2
1
3
212
KKKOHKKOHKOH
OHKKOHFe
(20)
32121
2
1
3
3213
KKKOHKKOHKOH
KKKFe
(21)
iii) Protolithic water theory
The dissociation constant of water determines the relationship between molar
concentration of 𝐻+ and 𝑂𝐻− in water at a specific temperature. Equations 22 and
23 show the chemical and mathematical interpretation of protolithic theory of water.
For convenience, the concentration of 𝐻+ is usually expressed in terms of pH,
21
equation 24. The dissociation constant of water are estimated using the temperature-
dependent empirical equation (Appelo & Postma, 1999).
OHHOH2 (22)
OHHKw (23)
HpH 10log (24)
iv) Total alkalinity
Alkalinity is defined as the ability of water to neutralize acids. It expresses the
excess of proton donors over the proton acceptors (Wolf-Gladrow, Zeebe, Klaas,
Körtzinger, & Dickson, 2007). Alkalinity also reflects the excess of chemical bases
of the solution relative to an arbitrarily specified zero level, or equivalent point
(Munhoven, 2013). Total alkalinity (TA) can be determined with higher accuracy
using complex equations, such as equation 25.
Ideally, the TA represents the amount of bases contained in a sample of the
natural water that will accept a proton when a sample is titrated with a strong acid
to the carbonic acid end point. The carbonic acid end point is the point where the
hydrogen protons 𝐻+ become more abundant than hydrogen carbonate ions 𝐻𝐶𝑂3−.
The carbonic acid end point is close to a pH equal 4.3. AMD samples may present
negative alkalinity, meaning that a strong base instead of a strong acid must be
added to reach the carbonic acid end point (Munhoven, 2013).
......2
22
434
2
3
43
3
4
2
44
2
33
POHHFHSOHSHSNH
SiOHPOHPOOHOHBCOHCOTA (25)
The alkalinity as defined above is a conservative quantity with respect to mixing
in water, and with respect to changes in temperature and pressure (Wolf-Gladrow,
Zeebe, Klaas, Körtzinger, & Dickson, 2007). Normally, in natural waters the
carbonate alkalinity is the most important part of the TA. Equation 25 can therefore
be reduced to equation 25a.
HOHCOHCOTA 2
33 2 (25a)
Equation 26 expresses total alkalinity as function of concentration of hydrogen
protons. The equation is obtained combining equations (3)-(9), 23, and 25a.
22
][][][][
2][
211
2
211
H
H
KTIC
KKHKH
KKHKTA w
aaa
aaa (26)
The other common concept of alkalinity states that total alkalinity is the ability
of water in capturing hydrogen protons, if only carbonic acid and iron hydroxide
reactions have significant influence on pH and alkalinity. Based on this presumption
the TA is calculated using equation 27 (Paper V).
HOHOHFeOHFeOHFeCOHCOTA2
23
2
33 (27)
Equation 27 also can be written as a function of concentration of hydrogen
protons, equation 28. This is accomplished combining equations (3)-(9), (13)-(21),
23 and 27.
][][
][][][
][][2
][3
][][
2][
321212
2
13
3
212
2
13
3
211
2
211
HH
Kw
KKKH
KwKK
H
KwK
H
Kw
H
KwKK
H
KwK
H
Kw
kkHkH
kkHkTA
aaa
aaa
(28)
v) Major ions
Major ions are the ions that usually appear in significantly larger concentrations
than other ions. In river water these ions are: 𝑁𝑎+, 𝐾+, 𝑀𝑔2+, 𝐶𝑎2+, 𝐻𝐶𝑂3−, 𝑆𝑂4
2−,
𝐶𝑙−, and 𝑁𝑂3− (Murray, 2004). Average concentrations of these ions per continent
were estimated and made available (Livingstone, 1963).
The average concentrations of major ions were converted to eq/l and further, the
concentrations in eq/l were converted to relative concentration of major ions in
percentage, table 1. Relative concentration of major ions is the percentage of each
ion in relation to the total concentration of positive ions in case of positive ion, and
in relation to total concentration of negative ions in case of negative ion (Paper II).
It was demonstrated that the relative concentration of major ions does not change
considerably over time (Paper II). This was confirmed by evaluating the trends using
the Man–Kendell test together with linear regression. Using Man–Kendell test and
a significance level of 0.05 it was found that, there is sufficient evidence to conclude
that there is no trend. The linear regression showed that the changes in relative
concentrations during a period of 10 years did not exceed 10% (Paper II).
23
vi) Solubility
The solubility of minerals determined by solubility constants is illustrated using
a hypothetical mineral (𝐴𝐵2). Equations 29 and 30 are the chemical reaction of
dissolution and the solubility constant of the hypothetical mineral, respectively
(Appelo & Postma, 1999). Based on the solubility of the mineral, three different
dissolution states are defined. i) Non-saturated condition, when more solute can be
added to the solvent (water) without forming precipitate. ii) Saturated condition, is
the limit condition at which precipitate is immediately formed in case of addition of
a small amount of solute. iii) Super-saturated condition, when there is a precipitate
of mineral which cannot be dissolved in the solution.
BAAB 22
2 (29)
b
AB BAK 1022
2 (30)
vii) Conductivity
The conductivity of a water sample is determined by the contribution of each
dissolved solute as well as the interaction between them (Pawlowicz, 2008). The
interaction between the ions have a significant contribution only if the concentration
of total dissolved solids increase to high levels (Pawlowicz, 2008). For dilute
solutions, the conductivity factor per ion can be determined and used to estimate
total conductivity, equation 31 (Tolgyessy, 1993). Conductivity factors of major
ions are given in table 2.
n
i
iiestimated CfEC1
(31)
24
Table 1 Average relative concentration of major ions as a percentage (%). The values in the table represent the average value per continent and its variability around average value. In some cases the average concentration of certain ion is low and its variability include negative values. Note that, negative values of concentration are not possible. Consider only the positive part of the variability range (Murray, 2004) (Paper II).
Ions (%) North America South America Europe Asia Africa Australia World
NO3− 0.9 ± 5.5 1.5 ± 2.4 2.6 ± 6.2 0.7 ± 1.3 1.0 ± 7.8 0.1 ± 5.0 1.1 ± 4.7
Cl− 12.7 ± 27.6 18.2 ± 24.9 8.4 ± 25.2 14.2 ± 22.2 25.4 ± 20.5 33.0 ± 32.4 15.4 ± 25.5
SO42− 23.5 ± 31.7 13.2 ± 19.1 21.6 ± 25.6 10.1 ± 20.5 21.0 ± 19.6 6.3 ± 7.9 16.4 ± 20.3
HCO3− 62.9 ± 38.6 67.1 ± 28.1 67.4 ± 32.7 75.0 ± 32.6 52.6 ± 29.2 60.6 ± 30.2 67.1 ± 31.9
Sum 100 100 100 100 100 100 100
K+ 1.9 ± 3.2 7.2 ± 5.5 1.9 ± 9.1 0.0 ± 3.9 6.2 ± 12.7 6.2 ± 5.8 4.1 ± 6.8
Na+ 20.7 ± 22.6 24.5 ± 30.7 10.2 ± 24.0 33.7 ± 17.6 21.7 ± 26.1 21.7 ± 17.5 19.2 ± 31.1
Mg2+ 22.0 ± 10.9 17.6 ± 11.4 20.3 ± 31.9 22.3 ± 11.7 38.7 ± 17.9 38.7 ± 13.7 24.0 ± 16.3
Ca2+ 55.4 ± 20.0 50.7 ± 28.3 67.6 ± 34.3 44.0 ± 20.6 33.5 ± 21.6 33.5 ± 14.2 52.6 ± 23.2
Sum 100 100 100 100 100 100 100
Table 2 Conductivity factors of ions at low concentration (Tolgyessy, 1993) (Paper II)
Ions Ca2+ Mg2+ K+ Na+ HCO3− CO3
2− Cl− NO3− SO4
2−
Conductivity factor fi (μS/cm per mg /L)
2.60 3.82 1.84 2.13 0.715 2.82 2.14 1.15 1.54
25
4.2 Model 1- Estimating inorganic ions in surface
water
None of the models mentioned in the introduction to this chapter were developed
to deal with water quality in waters affected by acid mine drainage. It would be
useful to have a model based on pH to estimate the concentration of ions in water
since pH influences the solubility of minerals in water (Appelo & Postma, 1999).
There are relatively few studies about concentration changes of major ions (MI) in
rivers compared to minor ions and heavy metals. A thorough search of the literature
did not reveal any studies that include models to estimate the concentrations of MI
in rivers. An interesting but rather old inventory of the concentrations of MI in rivers
and lakes all over the world was carried out in the context of salt discharge to the
oceans (Livingstone, 1963). The study resulted in an estimate of the total amount of
salts discharged to the oceans by rivers and the average concentrations of MI in
rivers per continent (Clarke, 1924; Conway, Mean geochemical data in relation to
ocean evolution, 1942; Conway, The Chemical Evolution of the Ocean, 1943;
Livingstone, 1963) . It was also demonstrated that pH combined with electrical
conductivity and concentration of sulphate ions can be used to estimate
concentration of metals in AMD using statistical methods (Valente, Ferreira,
Grande, Torre, & Borrego, 2013). There is a possibility of developing a model that
can be used to estimate the concentration of major ions in water combining
theoretical concepts and relationships already studied (Paper II). Model 1 is a
process based model developed to estimate the concentration of major ions using
pH alkalinity and temperature.
4.2.1 Modelling methodology
Theoretical concepts and relationships as well as statistics are combined to
develop a model that estimates concentration of major ions using pH, alkalinity and
temperature. Theoretical concepts and relationships that were used include: (i)
carbonate equilibrium; (ii) total alkalinity; (iii) statistics of MI; (iv) solubility of
minerals; and (v) conductivity as function of major ions in water (Paper II).
Concentration of 𝐻+, 𝑂𝐻−, H+, 𝐶𝑂32−, 𝐻𝐶𝑂3
− and 𝐻2𝐶𝑂3 is estimated by the
model using pH, alkalinity, and temperature. Further, concentration of major ions
(𝑁𝑎+, 𝐾+, 𝑀𝑔2+, 𝐶𝑎2+, 𝑆𝑂42−, 𝐶𝑙−, and 𝑁𝑂3
−) are estimated based on concentration
of 𝐻𝐶𝑂3− and relative concentrations of major ions in the base month (base month
- the month in which the data to calibrate the model is collected and the first
26
estimation is done). The model has two options to perform simulations, the
customized and generalized methods, distinguished by the data used to calibrate the
model (Paper II). The customized method uses the river specific relative
concentration of major ions of the base month to calibrate the model while
generalized method uses default relative concentrations of major ions per region
(Africa, North America, South America, Europe, Asia, Australia, or the “world”),
table 1. The option “world” can be used for any region and it is possible to get an
idea of which option (regional or world) is giving the better estimates by comparing
the difference between estimated and measured electric conductivity (DiffEC). The
model also estimates the total hardness as the sum of the concentrations of 𝑀𝑔2+
and 𝐶𝑎2+.
The third part of the model uses equilibrium equations to estimate the
concentrations of iron, manganese, and some heavy metals (Paper II). The main
purpose of estimating heavy metals is to get maximum possible concentrations to
use as an indication to decide whether there is a need for taking field samples for
more accurate analyses. The algorithm of the model is shown in Figure 9.
Figure 9 Algorithm of model 1. (adapted from Paper II).
Get continental average concentration of major ions in percentage from the database
Input data ( pH, alkalinity, temperature and electrical conductivity)
Calculate: [OH-], [H+], [OH-][HCO3-], [CO3
2-]
Input river specific baseline average concentration of major ions in percentage
Calculate: [Fe3+], [Mn2+], [Cd2+], [Cu2+],[Al3+], [Pb2+], [Zn2+]
Part I
Part II
Part III
no
Is there any
baseline data
yes
Calculate: [Mg2+], [Ca2+], [Na+], [K+], [Cl-], [SO4
2-], [NO3-], DiffEC
Output data {[OH-], [H+], [OH-], [HCO3-],
[CO32-], [Mg2+], [Ca2+], [Na+], [K+], [Cl-],
[SO42-], [NO3
-], [Fe3+], [Mn2+], [Cd2+], [Cu2+], [Al3+], [Pb2+], [Zn2+], DiffEC}
27
4.2.2 Evaluation of performance of model 1
Two parameters were used to evaluate the model performance, the difference
between the measured and estimated electric conductivity as a percentage (DiffEC)
and the Root mean square error (RMSE). DiffEC is used internally, within the
model to evaluate the modelled results while RMSE is used as an external tool to
evaluate the model performance in this study. The correlation coefficient R is also
used to compare the process based model suggested here with artificial neural
networks based model.
i) Difference between the measured and estimated electric conductivity
as a percentage DiffEC
A parameter to evaluate the estimated concentration of ions is included in the
model. The parameter is the difference between the measured and estimated electric
conductivity in percentage DiffEC, equation 32.
%100(%)
measured
estimatedmeasured
EC
ECECDiffEC (32)
Ideally, if all ions were included in the model, this value should be zero; however,
the model estimates the electric conductivity using only the major ions. The value
should therefore always be higher than zero, since some ions are left out in the
model. Sometimes the model may get DiffEC less than zero, implying that it is
underestimating the concentrations of ions with low electric conductivity factors
(bicarbonate, sulphate, nitrate, or potassium) or overestimating the ions with high
electric conductivity factors (magnesium, calcium, chlorine or sodium), table 2.
Even if the concentrations of ions with high electric conductivity are overestimated,
the DiffEC may still be positive when the concentration of the ions not considered
by the model is high.
When there is baseline data, the customized method is favourable to estimate the
concentrations of ions because it uses site specific data for calibration. The value of
DiffEC for the base month (or the month in which data was collected to calibrate
the model) should be higher than zero. The value of DiffEC for the base month
shows the relationship between the major ions and the ions not considered by the
model.
ii) Root mean square error (RMSE)
Root mean square error was used to compare the modelled and measured value
of concentration of major ions, equation 33. RMSE relative to the minimum
28
[RMSEmin (%)] and maximum [RMSEmax (%)] measured value as a percentage
were also used to quantify the error of estimates, equations 34 and 35, respectively.
n
i
ii nCCRMSEcalcmeas
1
2)(.
(33)
where, 𝐶𝑚𝑒𝑎𝑠 is the measured concentration of ions, 𝐶𝑐𝑎𝑙𝑐 is the modelled value of
the concentration and 𝑛 is the number of samples used to evaluate the model.
100min(%)min,
measC
RMSERMSE (34)
100max(%)max,
measC
RMSERMSE (35)
4.2.3 Results and discussion
Data from four stations in Swedish Rivers was used to test the model. The rivers
stations are: Skellefte älv, (Slagnäs), Vindelälven, (Maltbrännan), V. Dalälven,
(Mockfjärd), and Klarälven, (Edsforsen). The selection of the Swedish rivers was
justified by the availability of comprehensive data covering a long period of time.
Although the focus of the present study was to develop a method to be applicable in
developing countries, the governing laws for equilibrium concentration are
universal and not site specific, which implies that a comprehensive data set from
any river is suitable for testing the model.
Both modelling methods were tested, the generalized and the customized method.
As stated before, the generalized method uses continental averages, default data, to
calibrate the model when river specific data is not available. The customized method
uses a single measurement of relative concentrations of major ions in the base month
or an average of one year of measurements of relative concentration of major ions
to calibrate the model.
The values of RMSE for the customized method are between 0 and 67%, but
about 80% of the RMSE values are below 15%, for the four stations used in the
model validation (Paper II). For the generalized method, the corresponding RMSE
(%) values are between 0 and 101% and about 80% of the RMSE values are below
50% (Paper II). The analysis of RMSE was carried out excluding nitrate because its
estimates exhibit larger errors, RMSE higher than 150%. The RMSE analysis
demonstrate that the customized method gives better results than the generalized
29
method, as expected. The model works better to estimate the concentrations of ions
with relatively higher concentrations. For nitrate, which, in general, has lower
concentrations at all four monitoring stations compared to the other ions, the
modelled concentration values are quite different from the measured values. The
other reason why the model does not work well for nitrate is that nitrogen in surface
water is governed by many factors and the pH, alkalinity and temperature are not
enough to capture completely the effect of those factors. The factors include the
increasing concentration of nitrogen in river in later autumn, reaching its peak in
spring that is explained by the increasing losses from soils and low biological
activity in rivers (Laznik, Stalnacke, & Grimvall, 1999). The lower concentration of
nitrogen in summer and earlier autumn is caused by consumption by phytoplankton;
nitrogen uptake by crops and other biota; and denitrification processes in soil and
groundwater (Laznik, Stalnacke, & Grimvall, 1999).
The values of DiffEC for the generalized method varied between −15% and
+40%, but for the customized method it did not go beyond ±20% in relation to the
baseline value at all four stations used to test the model. Therefore, it is
recommended that when doing estimates using the generalized method, the values
of DiffEC should be between −15% to +40% and when using the customized
method, it is recommended that the values of DiffEC do not go beyond ±20% from
the baseline value (Paper II). Employing the suggested limits on DiffEC there is an
80% probability of having an RMSE (%) below 15% using the customized method
and below 50% using the generalized method (Paper II). If the value of DiffEC goes
beyond the suggested limits, the first option is to gather data from the river of
interest to recalibrate the model; such deviations might be caused by disturbances
to the river system from pollution discharge due to mining or other activities. If the
value of DiffEC still remains out of the normal range, the model is not recommended
for the specific river; the reason could be that significant amounts of ions, other than
the major ions considered in the present model, cause considerable variability in the
relative concentrations of ions.
4.2.4 Comparing the model with Artificial Neural Networks
Traditional statistical and neural networks models can also be used to estimate
concentration of ions in water. It is relevant to know the advantages of using
statistical models compared to physical processes based model (PPBM) suggested
here. It has been shown that under favourable conditions artificial intelligence
models such as artificial neural networks (ANN) perform better than traditional
statistical regression analysis (Paliwal & Kumar, 2009). The same data from four
Swedish Rivers was used to test the performance of ANN and PPBM; the values of
RMSE and correlation coefficient (R) were used to compare the results obtained
from the models.
30
Monthly data from 2001 to 2011 was used to develop and test the ANN model.
The data were divided into two parts; 60% to develop the model and 40% for testing
it. Using this division, 72 data samples were used for developing the model and 48
for the testing. The same data with 48 samples used to test the ANN model was used
to test the PPBM. Only the customized method, the most accurate one, in PPBM
was used and an average of two samples were used for calibration.
The model provided good estimates for all ions using both models in Skellefte
älv, at the Slagnäs station, except for nitrate (𝑁𝑂3−), see figures 10 and 11 (Paper
III). Similar results were obtained at the other three stations modelled. For ANN,
the RMSE (%) for all stations vary from 4 to 38 %, excluding nitrate, while the
values associated with nitrate are high, reaching values around 1000 (Paper III). For
PPBM the RMSE values for all stations vary from 4 to 71 %, excluding nitrate,
while the values associated with nitrate are high, reaching around 3000 (Paper III).
Figure 10 Concentration of positive ions in Skellefte älv at (Slagnäs station) [measured (meas.), estimated using physical processes based model (calc-PPBM.) and estimated using artificial neural networks (calc-ANN)] (Paper III)
The values of R show that the estimated and the measured values are well
correlated when using ANN, varying from 0.42 to 1.0, and the p-values associated
with the correlation coefficient are smaller than 0.05, implying that all correlation
coefficients are significant. While for PPBM the values of the correlation coefficient
are occasionally low, varying from 0.17 to 1.0 and the p-values associated with the
correlation coefficient are occasionally higher than 0.05.
An additional parameter to evaluate the quality of estimated values is available in
PPBM, the DiffEC. The values of DiffEC in the Skellefte älv at Slagnäs and
0
0,005
0,01
0,015
0,02
0,025
0,03
0,035
0,04
1 3 5 7 9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
CO
NC
EN
TR
AT
ION
(m
eq/l
)
MONTHS
Mg (meas.) Mg (calc-Theo.) Mg (calc-ANN)
0
0,02
0,04
0,06
0,08
0,1
0,12
0,14
0,16
0,18
1 3 5 7 9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
CO
NC
EN
TR
AT
ION
(m
eq/l
)
MONTHS
Ca (meas.) Ca (calc-Theo.) Ca (calc-ANN)
0
0,002
0,004
0,006
0,008
0,01
0,012
1 3 5 7 9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
CO
NC
EN
TR
AT
ION
(m
eq/l
)
MONTHS
K (meas.) K (calc-Theo.) K (calc-ANN)
0
0,005
0,01
0,015
0,02
0,025
0,03
0,035
0,04
0,045
0,05
1 3 5 7 9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
CO
NC
EN
TR
AT
ION
(m
eq/l
)
MONTHS
Na (meas.) Na (calc-Theo.) Na (calc-ANN)
calc-PPBM calc-PPBM
calc-PPBMcalc-PPBM
31
Vindelälven at Maltbrännan have a span of 13 and 34, respectively, and the
estimated values are better compared to Klarälven at Edsforsen and V. Dalälven at
Mockfjärd stations which have a span of 56 and 57, respectively (Paper III). As
stated previously, it is recommended that the values of DiffEC do not go beyond
±20% from the baseline value (Paper II). The PPBM should have been recalibrated
when the results started to exhibit value of DiffEC outside the recommended range.
However, the model was not recalibrated since the task was to compare the models
performance for the same conditions and data.
Figure 11 Concentration of negative ions in Skellefte älv at (Slagnäs station) [measured (meas.), estimated using physical process based model (calc-PPBM.) and estimated using artificial neural networks (calc-ANN)] (Paper III)
When there is enough historical data it is recommended to use the ANN model
combined with PPBM. This is because even if the ANN model gives better results
there is no way to check the accuracy of the estimates, whereas the PPBM can rely
on DiffEC for this purpose. The PPBM might be the only option when there are no
historical data to develop the ANN model; also, the PPBM is still able to provide
information about the quality of the estimates through the value of DiffEC. This
favours the application of PPBM in developing countries where there is limited
historical data due to poor monitoring programs resulting from lack of resources.
0
0,005
0,01
0,015
0,02
0,025
0,03
1 3 5 7 9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
CO
NC
EN
TR
AT
ION
(m
eq/l
)
MONTHS
Cl (meas.) Cl (calc-Theo.) Cl (calc-ANN)
0
0,005
0,01
0,015
0,02
0,025
0,03
0,035
0,04
0,045
1 3 5 7 9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
CO
NC
EN
TR
AT
ION
(m
eq/l
)
MONTHS
SO4 (meas.) SO4 (calc-Theo.) SO4 (calc-ANN)
0
0,02
0,04
0,06
0,08
0,1
0,12
0,14
0,16
0,18
1 3 5 7 9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
CO
NC
EN
TR
AT
ION
(m
eq/l
)
MONTHS
HCO3(meas.) HCO3 (calc-Theo.) HCO3 (calc-ANN)
0
0,0005
0,001
0,0015
0,002
0,0025
0,003
0,0035
1 3 5 7 9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
CO
NC
EN
TR
AT
ION
(m
eq/l
)
MONTHS
NO3 (meas.) NO3 (calc-Theo.) NO3 (calc-ANN)
calc-PPBM calc-PPBM
calc-PPBMcalc-PPBM
32
4.3 Model 2 - pH and alkalinity in streams
Because of rivers impacted by acidification (Anawar, 2015; DPLF, 2014; ICMM,
2012; Ochieng, Seanego, & Nkwonta, 2010), the poor water quality monitoring
programs in developing countries (Paper I), and the lack of appropriate and simple
models to simulate acidification (Paper II) it is relevant to develop a new model that
simulates water quality changes in rivers impacted by acidic discharge.
Contamination of rivers by acidic discharges includes two stages: (1) near field
where the mixing of acidic discharge with the stream water takes place, the region
ends when the homogeneity in the cross-sectional area of stream and equilibrium
between alkalinity species are reached; and (2) far field, the region starts where the
near field ends until the pH and alkalinity in the stream remains almost constant,
figure 12.
Figure 12 A conceptual model of a main stream affected by a release of acidic water. Two regions are identified: (1) near field where intense mixing of acidic discharge and stream water takes place and (2) far field where mixing in the cross section is complete and concentration vary due to advection-dispersion and processes at the upper and lower boundaries (Paper V).
The near field and far field are modelled separately. In chapter 4.3.1 a model
which simulates pH and alkalinity in the mixing zone is presented. The model is
developed considering only carbonaceous alkalinity to allow easy demonstration of
the modelling approach and it was tested using laboratory experiments.
A complete modelling methodology for simulating pH and alkalinity in streams
is presented in chapter 4.3.2. However, the main purpose of this chapter is to present
a model for simulating pH and alkalinity in the far field an extension of a model to
estimate pH and alkalinity at the near field is demonstrated by including the effect
of iron (III). The model was not tested with measured data. However, a discussion
Modelling
Sub-Model 2
*Ongoing work
CaCO3
CO2
pH and Alkalinity
33
about the validity of the model concepts used and quality of the model results is
presented based on a simulation of a hypothetical case.
4.3.1 Simulating pH and alkalinity in the mixing zone
A simple and easy-to-use physical process based model that simulates pH and
alkalinity in the near field, mixing zone is proposed. A model that considers
equilibrium between the alkalinity species in water but does not consider
equilibrium with 𝐶𝑂2 in the atmosphere and stream bed minerals at the mixing zone
is developed to overcome the limitations of available models in simulating
acidification of streams.
For modelling purpose, complete and instantaneous mixing is assumed, that is, a
completely stirred (CS) mixing zone when acidic water is discharged into the water
body. Homogeneity in the cross-sectional area and equilibrium between the
alkalinity species within the stream is reached immediately after discharge of acidic
water. This implies that the mixing time and the length of the mixing zone is zero;
thus, the effect of the surrounding environment (bottom minerals and atmospheric
gases) is neglected. There might be parts of the stream where the real pH before
mixing is complete might be lower than the pH estimated assuming completely
stirred due to effect of zonation in large streams (Schemel, Cox, Runkel, & Kimball,
2006). That cannot be compared to the effect of zonation because the processes are
slow but neglecting the effect of surrounding environment on pH and alkalinity will
make the real resulting pH when the mixing is complete slightly higher than the one
estimated assuming complete stirred.
4.3.1.1 Modelling methodology
In the development of the model, the volumetric flows are denoted by Q1, Q2, and
QR for the upstream river, acidic discharge, and downstream river, respectively, see
Figure 13. Volumes can replace the flows when simulating acidification of lagoons,
or other similar water bodies.
Figure 13 Schematical representation of simulated conditions where an acidic discharge is released to stream. CS = completely stirred (Paper IV)
CS
Main stream (Q1)
Acidic stream (Q2)
Stream after mixing (QR)
34
The main principle used for the development of the model are that the total
alkalinity (TA) and total inorganic carbon (TIC) are conservative with respect to
mixing. Thus, when Q1 and Q2 are mixed the TA and TIC can be added in moles.
The resulting total alkalinity (TAR) and total inorganic carbon (TICR) in the resulting
stream can be calculated using equations 36 and 37, respectively.
21
2211
QTAQTATAR
(36)
21
2211
QTICQTICTICR
(37)
Knowing the resulting total alkalinity and total inorganic carbon equation 26, can
be used to get the resulting concentration of hydrogen ions in equilibrium. Equation
26 can be written as a function 𝑓([𝐻+] = 0, equation 38. Which is solved
numerically using an iterative approach.
0][][][][
2][][
211
2
211
H
H
KTIC
KKHKH
KKHKTAHf w
R
aaa
aaaR
(38)
Newton-Raphson was selected to solve the equation where improved value of
[𝐻+] is determined using equation 39. The derivative of the function is calculated
using equation 40. Concentration of other alkalinity species are calculated using
equations (4)-(6).
i
iii
Hf
HfHH
1 (39)
01][][][
][4][][
22
211
2
2
2
121
2
1
H
KTIC
KKHKH
KKHKKHKHf w
R
aaa
aaaaa (40)
The calculation steps of the full model are given in the flow chart, figure 14. The
model is based on input of flows of the streams (𝑄1 and 𝑄2), pH of the streams (𝑝𝐻1
and 𝑝𝐻2), alkalinity of the streams ( 𝑇𝐴1 and 𝑇𝐴2), and the average water
temperature (𝑇). The model uses as a default value for temperature 25ºC, which can
be adjusted if necessary. A function 𝑓([𝐻+] = 0, obtained from the theories of
carbonate speciation and 𝑝𝐻 in water is solved using the Newton-Rapson method.
The output of the model is 𝑝𝐻 and 𝑇𝐴 of the resulting stream (𝑝𝐻𝑅 and 𝑇𝐴𝑅), as
well as the carbonate alkalinity species.
35
Figure 14 Flow diagram of the model that estimates pH (pHR) and alkalinity (TAR) resulting from the mixing of two streams with different pH and alkalinity (Paper IV)
4.3.1.2 Results and discussion
Mixing of two hypothetical streams with the flows 𝑄1 and 𝑄2 is used to evaluate
if modelled values correctly represent the buffer effect of carbonic acid in water. A
broad range of 𝑝𝐻 (12 to 1.5) was used in order to evaluate the model performance
for high, medium, and low values of 𝑝𝐻. An alkalinity of 0.086 eq/l was used to
allow for the visualization of the buffer effect.
Figure 15 shows that as the flow of acidic water (𝑄2) increases, the 𝑝𝐻 of the
resulting stream, 𝑝𝐻𝑅 tends to remain constant in three different section, between
𝑝𝐻 (12-9), (7-5) and (3-1.5) (Paper IV). Between these three sections there are two
intervals where the 𝑝𝐻 drops rapidly with the addition of small amounts of acidic
water 𝑄2. The two intervals where 𝑝𝐻 drops with only a small addition of acidic
water show the total conversion of 𝐶𝑂32− to 𝐻𝐶𝑂3
− and 𝐻𝐶𝑂3− to 𝐻2𝐶𝑂3,
respectively. The first two sections in figure 15, where the 𝑝𝐻 tends to remain
constant when acidic water is added, is due to the buffer effect of carbonic acid,
whereas the third section is only due to the dilution effect, showing that the 𝑝𝐻 of
the resulting stream tends to be equal to the 𝑝𝐻 of the acidic stream 𝑄2. These results
show that the model captures well the buffer effect of carbonic acid in water.
Calculate, TAR and TICR
Input data ( Q1, Q2, pH1, pH2, TA1, TA2, temperature (T))
Output data: TAR, pHR
Calculate the equilibrium constants Ka1, Ka2 and Kw.
Initial values: H(0) = Kw; i=0
Calculate the function and the derivative of function f([H+]), f’([H+])
error
Calculate pHR
Calculate TIC1 and TIC2
Calculate H(i+1)
Calculate the error:
%100
)1(
)()1(x
iH
iHiHerror
36
Figure 15 Results showing pHR vs Q2/Q1, where Q1 (pH =12, alkalinity = 0.086 eq/l) and Q2 (pH=1.5, alkalinity = -0.032 eq/l) are from two streams mixed in different proportions. pHR is the pH of the stream resulting from the mixing of Q1 and Q2 (Paper IV).
The change of concentration of carbonate species (𝐻2𝐶𝑂3, 𝐻𝐶𝑂3−, 𝐶𝑂3
2−), 𝑇𝐴,
and 𝑇𝐼𝐶 is as expected; see figure 16 (Paper IV). The 𝑇𝐼𝐶 at any 𝑝𝐻 is the sum of
inorganic species but it diminishes with the reduction of 𝑝𝐻. This is because the
𝑇𝐼𝐶 in the stream 𝑄2 is lower than the 𝑇𝐼𝐶 in the stream 𝑄1. The 𝑇𝐴 reduces with
the reduction of 𝑝𝐻 reaching zero at 𝑝𝐻 4.3. After 𝑝𝐻 4.3 the alkalinity has been
totally consumed. The negative value of 𝑇𝐴 shows that the water is getting even
more acidic.
Figure 16 Concentration of carbonic acid (H2CO3), bicarbonate (HCO3-), carbonate (CO3
2-), TICR, and TAR vs pHR in eq/l. pHR is the pH of the stream resulting from mixing of Q1 and Q2, where Q1 (pH =12, alkalinity = 0.086 eq/l) and Q2 (pH=1.5, alkalinity = -0.032 eq/l) are from two streams mixed with different proportions (Paper IV)
37
• Comparing modelled results with laboratory experiments
Six experiments were performed yielding validation data for the model; see table
3. The model was run to simulate 𝑝𝐻 and alkalinity for a river in the mixing zone
considering (1) a change of volumetric flow in the acid discharge while 𝑝𝐻 is
assumed constant and (2) a change in 𝑝𝐻 of the acidic discharge while the
volumetric flow is assumed constant. In both cases the main stream river flow is
assumed to be constant (Paper IV). The modelled results were compared with the
laboratory measurements using the correlation coefficient (R) and the associated
significance level, the p-value, and the Nash-Sutcliffe Efficiency (NSE), equation
41.
Table 3 Overview of laboratory experiments. For laboratory experiments V1, representing river water before contamination, and V2 ,representing acidic discharge, are equivalent to Q1 and Q2 in the model (adapted from Paper IV)
Simulation Scenario Exp. acidic water reactants (V2) basic water reactants (V1)
(1) change of volumetric flow in the acid discharge while pH is assumed constant
1 Deionized water + HCl Deionized water + NaOH (alkalinity = 0.0093 eq/l)
2 Deionized water + HCl Deionized water + NaOH + Na2CO3 (alkalinity = 0.054 eq/l)
3 Tap water + H2SO4 Tap water+ NaOH (alkalinity = 0.012 eq/l)
4 Tap water + H2SO4 Tap water+ NaOH+ Na2CO3 (alkalinity = 0.033 eq/l)
(2) change in pH of the acidic discharge while the volumetric flow is assumed constant
5 Deionized water+ HCl (pH varying high values to low)
Deionized water + NaOH + Na2CO3
6 Tap water + H2SO4 (pH varying high values to low)
Tap water+ NaOH+ Na2CO3
n
i
measmeas
i
n
i
i
meas
i
yy
yy
NSE
1
2
1
2mod
1 (41)
Where, 𝑛 is the total number of observations, 𝑦𝑖𝑚𝑒𝑎𝑠 is the value measured in each
experiment, 𝑦𝑖𝑚𝑜𝑑 is the corresponding modeled value, and 𝑦𝑚𝑒𝑎𝑠̅̅ ̅̅ ̅̅ ̅̅ is the average of
the experimental values (Taylor, He, & Hiscock, 2016).
Thus, NSE describes the “goodness-of-fit” between the experimental and
modeled values. It can vary from -∞ to 1, where the value of 1 represents a perfect
fit. A value between 0 to 1 is generally recognized as acceptable model performance,
whereas a value less than zero means that the average of the measured values is a
better predictor of a variable compared to the model, indicating unsatisfactory model
performance (Taylor, He, & Hiscock, 2016).
38
Figures 17 and 18 show the predicted and measured values for the first simulation
scenario using (1) deionized water and 𝐻𝐶𝑙, and (2) tap water and 𝐻2𝑆𝑂4,
respectively, for two conditions, one with low alkalinity and the other one with high
alkalinity (Paper IV). The figures show that the modelled pH and alkalinity agree
well with the measured values. However, the measured alkalinity in the experiments
with tap water and 𝐻2𝑆𝑂4 is below the alkalinity estimated by the model. In the high
alkalinity experiment the difference is about 0.02 eq/l at higher pH values, figure
18.b. This difference is related to the presence of 𝐻𝑆𝑂4− introduced by the sulfuric
acid used to produce acidic water in the experiments that is not considered in the
model, see equation 25.
Figure 17 Model prediction and measured values of a) pH and b) alkalinity. The results correspond to experiments (1) and (2) in table 3. pHR is the pH resulting after mixing V1 and V2. (Paper IV)
Figure 18 Model prediction and measured values of a) pH and b) alkalinity. The results correspond to experiments (3) and (4) in table 3. pHR is the pH resulting after mixing V1 and V2 (Paper IV).
Figures 19 and 20 show the modelled and measured values for the second
simulation scenario using (1) deionized water and 𝐻𝐶𝑙, and (2) tap water and
𝐻2𝑆𝑂4, respectively (Paper IV). The figures show that the modelled pH and
a) b)
a) b)
39
alkalinity agree well with the measured values. In the 𝑝𝐻 change experiment the
modelled and measured resulting alkalinity differ at low 𝑝𝐻, figure 20.b. This
happens because the experiments were performed differently. For the 𝑝𝐻 change
experiments, the initial samples were both prepared with high 𝑝𝐻, while for the
volume change experiments the initial samples were prepared one with high 𝑝𝐻 and
the other with low 𝑝𝐻. For the 𝑝𝐻 change experiments, the 𝑝𝐻 was lowered by
adding acidic water (prepared with 𝐻2𝑆𝑂4).
Figure 19 Model prediction and measured values of a) pH and b) alkalinity. The results correspond to experiment (5) in table 3. pHR is the pH resulting after mixing V1 and V2 (Paper IV).
Figure 20 Model prediction and measured values of a) pH and b) alkalinity. The results correspond to experiment (6) in table 3. pHR is the pH resulting after mixing V1 and V2 (Paper IV).
The correlation coefficients in all experiments are significant at a confidence level
of 0.95, table 4. Calculated p-values for all correlation coefficients are much less
than 0.05. NSE values are between 0 and 1 for all experiments. The correlation
coefficient together with NSE values reveal that the model is accurate enough to be
a) b)
a) b)
40
used for practical applications, table 4 (Paper IV). An example of such a practical
application is given in chapter 4.3.1.3.
Table 4 Correlation coefficient (R) and Nash-Sutcliffe Efficiency (NSE) values for experiments 1 to 6 expressing the goodness-of-fit of the model compared with measured pH and alkalinity (Paper IV)
Experiment
pH Alkalinity
R NSE R NSE
1 0.95 0.84 0.99 0.92
2 0.99 0.99 0.98 0.88
3 0.99 0.98 0.99 0.98
4 0.98 0.97 0.99 0.98
5 0.86 0.71 0.80 0.90
6 0.94 0.54 0.86 0.59
4.3.1.3 Application of the model for Zambezi River Basin
The task here is to evaluate the threshold pH in the effluent from the mining area
that may trigger significant changes in the pH in the Zambezi River. To address this
question, the model developed in the present study is used to simulate change in pH
in the main stream of Zambezi River as a result of change in 𝑝𝐻 of incoming waters
from the mining area. For the simulation, the 𝑝𝐻 in the effluent from the mining
area is assumed to vary from 7.85 to 2. The average flow, 𝑝𝐻, and alkalinity of both
the main stream and the tributaries from the mining area are given in table 5. At
present, there is no contamination reported in the main stream that indicates
acidification (Nhantumbo, Evaluation of Long-term Impact of Coal Mining in
Zambezi River Basin in Mozambique, 2013).
Tabel 5 Average flow, pH and alkalinity of the main stream of Zambezi River Basin upstream the mining area and tributaries coming from the mining area (Nhantumbo, Evaluation of Long-term Impact of Coal Mining in Zambezi River Basin in Mozambique, 2013) (Paper IV)
Parameter Flow (m3/s) pH Alkalinity (mg/l as CaCO3)
Main stream 2330 7.6±0.3 62±2 (0.00124 eq/l)
Tributaries 1120 7.85±0.4 129±102 (0.00384 eq/l)
The results of the simulation show that when average 𝑝𝐻 of the water in the
incoming tributaries from the mining area is about 3, the 𝑝𝐻 in the main stream of
Zambezi River drops from about 6, to 3, Figure 21 a) (Paper IV). This shows that
with the present alkalinity and flows, the main stream of Zambezi River cannot
support 𝑝𝐻 drops in waters coming from the tributaries of the mining area to values
below 3. Additional analysis has been done using the speciation of carbonate ions,
𝑇𝐼𝐶, and 𝑇𝐴 from figure 21 b). By comparing figures 21a) and b) it is possible to
see that the 𝑝𝐻 drops when the alkalinity in the main stream is totally consumed.
41
Figure 21 Simulated a) resulting pH [pHR] in the main stream of Zambezi River (pH2) and b) concentration of carbonaceous alkalinity species, total inorganic carbon (TIC), and total alkalinity (TA), against pH in the water coming from the mining area (Paper IV).
The pH of the water coming from the mining area should not decrease to values
below 3 to avoid significant pH drop in the main stream of the river. However, this
does not guarantee that the water is not impacted. The tributary water with 𝑝𝐻 3,
depending on the geology of the area, could probably contain a high quantity of
dissolved heavy metals that may impact the water of the main stream, even though
the 𝑝𝐻 is still above 6.5.
As the tributaries connect to the river in different points along the mining area,
the scenario described above might occur only if the there is no 𝐶𝑂2 degassing to
the atmosphere or buffer minerals being dissolved at the bottom of the stream. At
least 𝐶𝑂2 degassing will take place after each tributary is joining and there is a
chance of having buffer mineral at the bottom of the stream. All these effects will
contribute to reduce the impact. There is also a chance of having zonation creating
localized parts of the river with extremely low pH values (Schemel, Cox, Runkel,
& Kimball, 2006), but this effect can only be understood with three-dimensional
hydraulic modelling, which is not here.
4.3.2 Methodology for simulating pH and alkalinity in streams
A modelling methodology for simulating pH and alkalinity in streams impacted
by acidic discharges is proposed considering both reactions and transport processes
as well as the equilibrium between the alkalinity species and the influence of the
surrounding environment. The methodology is meant to be used for simulating
contamination and for planning reclamation projects in streams already impacted.
The modelling methodology proposed is based on the pollutant transport equation
(advection-diffusion equation); equilibrium adjustment based on alkalinity species
in water, equations 26 and 28; and classical mass transfer modelling procedures for
modelling the influence of the surrounding environment, Figure 12. The modelling
a) b)
42
methodology suggested can be applied for simulating two different scenarios;
continuous and non-continuous discharge of acidic water into streams. However,
the main purpose of this chapter is to develop a modelling methodology for the far
field (Paper V). The possibility of extension of the model for the near field, mixing
zone is demonstrated by including iron (III).
Figure 22 Calculation scheme, change of concentration with time. The concentration of alkalinity specie (1) at
position x and time t ( 𝑪(𝒙,𝒕),𝒆𝒒(𝟏)
) changes due to advection and diffusion as well as due to other processes (∆𝑪(𝒙,𝟏)(𝟏)
,
∆𝑪(𝒙,𝟐)(𝟏)
, …, and ∆𝑪(𝒙,𝒌)(𝟏)
) during the time step ∆𝒕, resulting in concentration of alkalinity specie (1) at position x
and time 𝒕 + ∆𝒕 (𝑪(𝒙,𝒕+∆𝒕)(𝟏)
). Similarly for concentration of alkalinity specie (2) changing its concentration from
𝑪(𝒙,𝒕),𝒆𝒒(𝟐)
to 𝑪(𝒙,𝒕+∆𝒕)(𝟐)
. These processes are simulated independently at each time step. After each the advection-
diffusion has been solved the equilibrium between all modelled alkalinity species (1, 2, …, m) is adjusted,
getting 𝑪(𝒙,𝒕+∆𝒕),𝒆𝒒(𝟏)
and 𝑪(𝒙,𝒕+∆𝒕),𝒆𝒒(𝟐)
. The notation ∆𝑪(𝒙,𝟏)(𝟏)
means the change of concentration of alkalinity specie (1)
at position x due to process 1 and ∆𝑪(𝒙,𝟐)(𝟏)
means the change of concentration of alkalinity specie (1) at position
x due to process 2 (Paper V).
A schematic representation of the modelling methodology in the “far field” is
given in figure 22 and 23. The change of concentration of alkalinity species with
time is due to advection and diffusion as well as the added effects of the surrounding
environment (other processes), figure 22. The change of concentration of alkalinity
species with space is due to advection and diffusion, figure 23. A complete scheme
representing both change of concentration of alkalinity species with time and space
is given in figure 24.
v
Other processes
)1(
),,( eqtxC)1(
),( ttxC
)1(
),,( eqttxC
)1(
)1,(
)1(
)2,(
)1(
),(
x
x
kx
C
C
C
)2(
),( ttxC
)2(
),,( eqttxC
)2(
)1,(
)2(
)2,(
)2(
),(
x
x
kx
C
C
C
)2(
),,( eqtxC
v
Equilibrium
adjustment
a)
)1(
),,( eqtxC )1(
),,( eqtxxC
)2(
),,( eqtxxC
)2(
),,( eqtxC
Advection-diffusion
Equilibrium
adjustment
Advection-diffusion
Advection-diffusion Advection-diffusion
Equilibrium
adjustment
Equilibrium
adjustment
Other processes
Advection-diffusion
Advection-diffusion
Advection-diffusion
Advection-diffusion
43
Figure 23 Calculation scheme, change of concentration with space. The concentration of alkalinity species (1)
and (2) ( 𝑪(𝒙,𝒕),𝒆𝒒(𝟏)
and 𝑪(𝒙,𝒕)(𝟐)
) are simulated as being influenced by advection and diffusion along the space step
∆𝒙 independently, after which the equilibrium between them is adjusted to get 𝑪(𝒙+∆𝒙,𝒕),𝒆𝒒(𝟏)
and 𝑪(𝒙+∆𝒙,𝒕),𝒆𝒒(𝟐)
. (Paper
V).
v
Other processes
)1(
),,( eqtxC)1(
),( ttxC
)1(
),,( eqttxC
)1(
)1,(
)1(
)2,(
)1(
),(
x
x
kx
C
C
C
)2(
),( ttxC
)2(
),,( eqttxC
)2(
)1,(
)2(
)2,(
)2(
),(
x
x
kx
C
C
C
)2(
),,( eqtxC
v
Equilibrium
adjustment
a)
)1(
),,( eqtxC )1(
),,( eqtxxC
)2(
),,( eqtxxC
)2(
),,( eqtxC
Advection-diffusion
Equilibrium
adjustment
Advection-diffusion
Advection-diffusion Advection-diffusion
Equilibrium
adjustment
Equilibrium
adjustment
Other processes
Advection-diffusion
Advection-diffusion
Advection-diffusion
Advection-diffusion
44
Figure 24 Schematic representation of the modeling methodology. The pollutant transport equation is used to simulate the advection and diffusion of each alkalinity specie. Small steps in time and space are taken because the alkalinity species are simulated as being transported independently. The reaction processes taking place during the transport process that may cause change in concentration of each alkalinity specie are considered at each time step. After each distance and time step the effect of advection and diffusion is added to the effect other process and the equilibrium between different alkalinity specie is then adjusted (Paper V).
)1(
),,( eqtxC)1(
),,( eqtxxC
)1(
),,2( eqtxxC )1(
),,)1(( eqtxnxC
)1(
),,( eqtxnxC
)1(
),( ttxC )1(
),( ttxxC
)1(
),2( ttxxC
)1(
),)1(( ttxnxC )1(
),( ttxnxC
)1(
)1,(
)1(
)2,(
)1(
),(
x
x
kx
C
C
C
)1(
)1,(
)1(
)2,(
)1(
),(
xx
xx
kxx
C
C
C
)1(
)1,2(
)1(
)2,2(
)1(
),2(
xx
xx
kxx
C
C
C
)1(
)1,)1((
)1(
)2,)1((
)1(
),)1((
xnx
xnx
kxnx
C
C
C
)1(
)1,(
)1(
)2,(
)1(
),(
xnx
xnx
kxnx
C
C
C
v vvvv
)1(
),,( eqttxC
)1(
),,( eqttxxC
)1(
),,2( eqttxxC )1(
),,)1(( eqttxnxC
)1(
),,( eqttxnxC
)2(
),,( eqtxC)2(
),,( eqtxxC
)2(
),,2( eqtxxC )2(
),,)1(( eqtxnxC
)2(
),,( eqtxnxC
)2(
),( ttxC )2(
),( ttxxC
)2(
),2( ttxxC
)2(
),)1(( ttxnxC )2(
),( ttxnxC
)2(
)1,(
)2(
)2,(
)2(
),(
x
x
kx
C
C
C
)2(
)1,(
)2(
)2,(
)2(
),(
xx
xx
kxx
C
C
C
)2(
)1,2(
)2(
)2,2(
)2(
),2(
xx
xx
kxx
C
C
C
)2(
)1,)1((
)2(
)2,)1((
)2(
),)1((
xnx
xnx
kxnx
C
C
C
)2(
)1,(
)2(
)2,(
)2(
),(
xnx
xnx
kxnx
C
C
C
v vvvv
)2(
),,( eqttxC
)2(
),,( eqttxxC
)2(
),,2( eqttxxC )2(
),,)1(( eqttxnxC
)2(
),,( eqttxnxC
45
4.3.2.1 Mixing
Mixing of an acidic effluent and stream water before transport is simulated using
the principles described and demonstrated to be valid for simulating pH and
alkalinity in the mixing zone in chapter 4.3.1. The total alkalinity and total inorganic
carbon are calculated using equations 36 and 37. Total iron (III) is calculated using
the same principle as for total alkalinity and total inorganic carbon being
conservative with respect to mixing, equation 42. The parameters in equation 42
refers to Figure 13.
21
2211
QTFeQTFeTFe R
(42)
Knowing the values of total alkalinity, total inorganic carbon and total iron, the
only unknown in equation 28 is the concentration of hydrogen protons. Equation 28
can be converted into a function 𝑓([𝐻+] = 0, equation 43. The function is solved
numerically using an iterative approach. The Newton-Raphson method is not
suitable for solving this function because it has sections where the derivative is zero,
therefore the bisection method was used. The concentration of hydrogen protons
calculated in this way is the resulting equilibrium concentration after mixing of
streams 𝑄1 and 𝑄2. Concentrations of other alkalinity species are calculated using
equations (4)-(6) and (14)-(17).
0][][
][][][
][][2
][3
][][
2][
321212
2
13
3
212
2
13
3
211
2
211
HH
Kw
TFe
KKKH
KwKK
H
KwK
H
Kw
H
KwKK
H
KwK
H
Kw
TICkkHkH
kkHkTAHf R
aaa
aaaR
(43)
4.3.2.2 Transport
Transport of carbonate alkalinity species (𝐻+, 𝑂𝐻−, 𝐻2𝐶𝑂3, H𝐶𝑂3− and 𝐶𝑂3
2− )
are simulated using the advection-diffusion equation, equation 44 solved
numerically using an explicit scheme (Benedini & Tsakiris, 2013) . The explicit
numerical scheme was selected because it allows coupling with models that simulate
other processes affecting 𝑝𝐻 in water and adjustment of chemical equilibrium
between the alkalinity species.
2
2
x
CE
x
Cu
t
C x
(44)
46
Where, 𝐶 is the concentration of the pollutant, 𝑥 position, 𝑡 time, 𝐸 dispersion
coefficient and 𝑢𝑥 velocity in 𝑥 direction.
Equation 45 is the numerical solution of equation 44. The parameters in equation
44 correspond to figure 25. Equation 46 defines the stability criterion for equation
45 (Benedini & Tsakiris, 2013). For modelling the user defines the space step (∆𝑥)
and the time step (∆𝑡) is calculated to guarantee that the stability criterion is
satisfied.
j
s
j
sj
s
j
s
j
sj
s Cx
E
x
UtC
x
E
ttC
x
E
x
UtC 12
1
212
11
2
21
2
(45)
Figure 25 Calculation scheme of numerical solution of advection-diffusion equation. 𝒔 refers to space and 𝒋 to time (Paper V).
12
20
2
2
x
tE
x
tU (46)
4.3.2.3 Other processes
In the far field, the alkalinity species are transported, and reactions continuously
adjust the equilibrium while the surrounding environment (other processes) also
affects the concentration of alkalinity species. Other processes include exchange of
gases between the atmosphere and stream water, dissolution of stream bed minerals
as well as the influence of sources and sinks. How to model sources and sinks is
described in hydraulics and water quality modelling books and it is not discussed
here (Benedini & Tsakiris, 2013). Modelling of gas exchange between stream water
and atmosphere as well as dissolution of stream bed minerals are processes
explained through mass transfer principles which are less discussed in surface water
modelling. Carbon dioxide, 𝐶𝑂2, and calcium carbonate, 𝐶𝑎𝐶𝑂3, are chosen to
demonstrate how to model gas exchange between stream water and atmosphere and
dissolution of stream bed minerals, respectively. Carbon dioxide 𝐶𝑂2 degassing and
1j
sU
1j
sC
j
sU 1
j
sC 1
j
sUj
sC
j
sU 1
j
sC 1
t
s
47
𝐶𝑎𝐶𝑂3 dissolution were chosen because they are two of the most important
processes influencing 𝑝𝐻 in natural waters; and 𝐶𝑎𝐶𝑂3 is commonly used in
reclamation projects in streams impacted by acidic discharges (Ziemkiewicz,
Skousen, Brant, & Lovett, 1997). Both 𝐶𝑂2 degassing and 𝐶𝑎𝐶𝑂3 dissolution are
simulated using classical mass transfer theories (Treybal, 1981; Foust, A., Clump,
Maus, & Anderson, 1980).
Carbon dioxide 𝐶𝑂2 degassing and 𝐶𝑎𝐶𝑂3 dissolution, can be described using
the mass balance, equation 47. Taking, 𝑎 = 𝑆/𝑉 where 𝑆, is the mass transfer area
and 𝑉 the volume of water of stream element; and 𝑁 = [𝑚𝑜𝑙𝑒𝑠
𝑚2𝑠] molar flux of the
solute considered. The change of number of moles in given control volume due to
moles of solute crossing the surfaces can be calculated using the molar balance,
equation 47.
tNxAaCCxA ttt )( (47)
Where, 𝐴 is the stream cross section area, and ∆𝑥 is equivalent to the length of
control volume. For an infinitesimal element of volume, the equation 47 can be re-
written as equation 48.
Nat
C
transfermass
)(
(48)
Equation 49 defines molar flux. Equation 50 is obtained replacing equation 49 in
equation 48.
)( CChN s (49)
CChat
Cs
transfermass
)(
(50)
Where: ℎ- is the mass transfer coefficient in 𝑚/𝑠, 𝐶𝑠 - is concentration of solute
at the interface (solid-liquid or liquid-gas), that is equivalent to saturation
concentration in 𝑚𝑜𝑙/𝑚3, 𝐶 - is the average concentration of solute in the stream
in given location in 𝑚𝑜𝑙/𝑚3. Equation 51 is obtained integrating the equation 50
from 𝑡 to 𝑡 + ∆𝑡 and 𝐶𝑡 to 𝐶𝑡+∆𝑡. The change of concentration of a certain specie
∆𝐶 due to the process described by equation 50 is obtained applying ∆𝐶 = 𝐶𝑡+∆𝑡 −𝐶𝑡 and 𝐶𝑡+∆𝑡 = ∆𝐶 + 𝐶𝑡 to equation 51, resulting in equation 52.
48
tha
tsstt eCCCC
(51)
tha
tstransfermass eCCC
1 (52)
i) Calcite dissolution
Calcite dissolution affects directly the concentration of [𝐶𝑂32−] in water, thus
affecting the total alkalinity and pH. Equation 53 is the chemical reaction of calcite
dissolution. The solubility constant is calculated by equation 53a. As the 𝐶𝑠 =[𝐶𝑎2+] = [𝐶𝑂3
2−], the saturation concentration depends only on solubility constant,
equation 54. The solubility constant of calcite at 25 degrees is found in chemistry
handbooks (Appelo & Postma, 1999).
2
3
2
3 COCaCaCO (53)
2
3
2 COCaKs (53a)
ss KC (54)
As 𝑎 = 𝑆/𝑉, 𝑆 = 𝑃 ∙ ∆𝑥 and 𝑉 = 𝐴 ∙ ∆𝑥, the mass transfer area per unit volume
is calculated using equation 55. Therefore, the change of concentration of 𝐶𝑂32− in
the stream due to calcite dissolution can be calculated using equation 56.
RA
Pa
1 (55)
Where: R is hydraulic radio, and P wetted perimeter.
thR
tscalcite
D
eCKC1
1 (56)
ii) Carbon dioxide degassing
Degassing or absorption of 𝐶𝑂2 affects the concentration of carbonic acid,
𝐻2𝐶𝑂3, in water, thus affecting the alkalinity and 𝑝𝐻. Concentration of carbonic
acid in surface water depends on partial pressure of 𝐶𝑂2 in the air (𝑝𝐶𝑂2), equation
57. When the stream is disturbed by adding acidic water there will be 𝐶𝑂2 exchange
with the atmosphere tending to a new equilibrium.
49
H
CO
COsK
pC 2
2, (57)
Where: 𝐾𝐻 is the henry constant, and 𝐶𝑠,𝐶𝑂2 is the saturation concentration of
𝐶𝑂2 in water. Concentration of carbon dioxide is related to the concentration of
carbonic acid in water through chemical reaction described by equations 58 and 58a.
Thus, the changes in concentration of carbonic acid in water within a time interval
∆𝑡, can be calculated using equation 59.
322,2 COHOHCO l (58)
2
32
CO
COHK (58a)
Where, 𝐾 is the equilibrium constant.
that
H
CO
idecarbondioxGe
K
COH
K
pKC
1322 (59)
If the river has a constant cross sectional area 𝐴 and width 𝑊, equation 60
calculates the mass transfer area per unit volume. Equation 61 gives the change of
concentration of 𝐻2𝐶𝑂3 in the stream water due to 𝐶𝑂2 degassing.
A
W
V
Sa (60)
thA
W
t
H
CO
idecarbondiox
G
eK
COH
K
pKC 1322 (61)
Where, ℎ𝐺 is the mas transfer coefficient of carbon dioxide.
Other similar processes can be modelled using the same procedure as for calcite
dissolution and carbon dioxide degassing. Mass transfer coefficients can be
estimated using correlations that have been developed based on momentum, mass,
and heat transfer analogies (Treybal, 1981; Foust, A., Clump, Maus, & Anderson,
1980). More accurate values of mass transfer coefficients can be determined
experimentally. For this modelling the mass transfer coefficients were estimated
using a correlation called Reynolds and Prandtl analogy, equation 62, (Treybal,
1981; Foust, A., Clump, Maus, & Anderson, 1980). Reynolds number (𝑅𝑒), and
Schmidt number (𝑆𝑐) are calculated using equations 63 and 64, respectively.
50
1Re1.21
Re03.01.0
2.0
Scu
h (62)
RuRe (63)
ABDSc (64)
Where, 𝑢 is the water velocity, 𝜇 is the water viscosity, 𝑅 is the hydraulic radio,
𝜌 is the water density, and 𝐷𝐴𝐵 is the diffusivity coefficient.
4.3.2.4 Equilibrium adjustment
The carbonaceous alkalinity species are simulated being transported separately.
After each calculation step the equilibrium between them is adjusted. The
equilibrium is adjusted after taking into consideration both advection-diffusion and
the effect of the surrounding environment (other processes) for each carbonaceous
specie, figures 22, 23 and 24. Equilibrium adjustment is done using the same
principle as the one used for simulating mixing, equation 43. If iron is present in the
water, its influence during transport is considered during the equilibrium
adjustment.
4.3.2.5 Analysis of model results
The pollutant transport equation for a conservative pollutant solved using an
explicit solution was previously demonstrated to be accurate enough for practical
applications (Benedini & Tsakiris, 2013). Simulating mixing of streams using the
principle of conservation of alkalinity and total inorganic carbon with respect to
mixing was also shown to yield good results (Paper IV). Carbon dioxide degassing
and calcite dissolution were modelled using a classical modelling procedure widely
used for modelling mass transfer processes (Foust, A., Clump, Maus, & Anderson,
1980; Treybal, 1981).
The model is tested for simulating pH and alkalinity in the near field, mixing zone
(Paper V). It was also tested for the far field with processes including transport,
carbon dioxide degassing, and calcite dissolution with equilibrium adjustment
between the alkalinity species for continuous and non-continuous discharge of
acidic water, Table 5 (Paper V). Table 6 gives the 𝑝𝐻, alkalinity and temperature of
the main stream and acidic discharge used for all simulations and Table 7 gives the
characteristics of the main stream.
51
Table 5 Hypotethic simulations done to evaluate the modelling methodology. AW=Acidic water (Paper V)
Type Simulation Main characteristic
Mixing 1 Without iron
2 With iron
Transport
Continuous discharge of AW
3 Without equilibrium adjustment
4 With equilibrium adjustment, calcite dissolution and CO2 degassing
Non-Continuous discharge of AW
5 Without equilibrium adjustment
6 With equilibrium adjustment, calcite dissolution and CO2 degassing
The pH, alkalinity, and temperature in table 6 are real data from Zambezi River
in Mozambique. The flowrate of both the hypothetical main stream and the acidic
discharge as well as the values of stream characteristics in table 7 were selected to
get reasonable value of the dispersion coefficient. Acidic water characteristics were
selected to allow easy visualization of the reaction due to iron (III) buffer effect,
occurring for pH below 4.3. Values of the mass transfer coefficient can be estimated
from the literature or measured experimentally (Foust, A., Clump, Maus, &
Anderson, 1980; Treybal, 1981). For the present modelling, the mass transfer
coefficients were estimated using equation 62. The values of diffusivities of 𝐶𝑂2
and 𝐶𝑂32−, water viscosity and density were taken at 25⁰C. The stretch of stream
used for the simulation had a 10-km length and the total simulation time was 2 hours.
For the non-continuous simulation, the acidic water discharge time used was 10
minutes. The space step for the numerical calculation was 2 meters. These
parameters were also selected to permit a clear illustration of the impact of the acidic
water discharge on the stream without having extremely long simulation times.
Table 6 Data used for hypothetic simulation. pH, alkalinity, temperature, and flowrate of acidic discharge, upstream the mixing zone and in the main stream before contamination (Paper V).
Upstream the mixing zone
Stream before discharge of acidic water
Acidic discharge
pH 7.9 7.9 3.5
Alkalinity (eq/l) 0.009 0.009 0.000
Temperature (⁰C) 25 25 25
Flow(m3/s) 1.94 - 0.2
When the main stream water and acidic discharge are mixed, table 6, there is a
significant difference of 𝑝𝐻 depending on whether iron is present or not in the acidic
water, table 8 (Paper V). Three simulations were done, the first without 𝐹𝑒3+, the
second with 0.09 eq/L of 𝐹𝑒3+, and the third with 0.3 eq/L of 𝐹𝑒3+ in the acidic
discharge. When the concentration of 𝐹𝑒3+ increases in the acidic discharge both
resulting 𝑝𝐻 and alkalinity decrease, as expected. The behaviour is explained by
𝐹𝑒3+ capturing 𝑂𝐻− radicals successively as 𝐹𝑒(𝑂𝐻)2+, 𝐹𝑒(𝑂𝐻)2+ and
precipitating as 𝐹𝑒(𝑂𝐻)3, thus reducing both the 𝑝𝐻 and alkalinity, equation 27.
52
Table 7 Stream characteristics used for hypothetic simulation. Stream width, cross section, wet perimeter and
dispersion coefficient (Paper V).
Width (m) 6
Cross section area (m2) 7.2
Wetted perimeter (m) 8.4
Dispersion coefficient (m2/s) 5
Table 8 pH and alkalinity resulting after discharging the acidic water in the near field. Simulations correspond to table 5 (Paper V)
Simulation Main characteristic pH Alkalinity (eq/l)
1. (without iron) 5.94 0.0081
2.
(with iron = 0.09 eq/l) 5.09 0.0015
(with iron = 0.3 eq/l) 4.25 0.0002
There is a significant difference when pH is simulated as a conservative pollutant
compared to when it is simulated with equilibrium adjustment, see figures 25 and
26 for the continuous and non-continuous discharge, respectively (Paper V). For the
case of continuous discharge of acidic water, the contamination front travels
downstream with pH between 5 and 7.9. These values are equal to the pH
immediately after mixing is completed and the pH in stream before contamination,
respectively (see figures 25a and 25b). This shows that the effect of the carbon
dioxide degassing and calcite dissolution is not significant during the first 2 hours
of simulation. However, the shape of the front of the polluted water for the case of
equilibrium adjustment (figure 25b) differs from the one without equilibrium
adjustment, see figure 25a. This is because when hydrogen ions together with other
ions considered (𝑂𝐻−, 𝐻2𝐶𝑂3, 𝐻𝐶𝑂3− and 𝐶𝑂3
2−) being transported are affected by
the dispersion creating a front with pH varying from 5 to 7.9. When carbonaceous
species are simulated separately, the concentrations in the front are not in
equilibrium and when the equilibrium between the them is adjusted there is a tilting
of the front upwards, see (figure 25c).
The effect of equilibrium adjustment is even more evident in non-continuous
discharge of acidic water (figure 26c) (Paper V). When simulating transport without
equilibrium adjustment, the minimum value of pH in the polluted water when it
travels downstream increases due to dispersion (figure 26a), tending towards the
original value of pH in the stream (pH =7.9). The same behaviour can be seen in the
simulation of all alkalinity species (𝐻+ , 𝑂𝐻−, 𝐻2𝐶𝑂3, 𝐻𝐶𝑂3− and 𝐶𝑂3
2−) without
equilibrium adjustment; they tend to the original value of its concentration in the
stream before contamination, as expected. Therefore, when adjusting equilibrium
between the alkalinity species the pH in the stream recovers more rapidly. After two
hours of simulation the pH recovers from 5 to 5.5 without equilibrium adjustment
(figure 26a) and from 5 to 6.2 with equilibrium adjustment (figure 26b).
The effects of carbon dioxide degassing and calcite dissolution are demonstrated
not to be significant for short simulation times for the simulated conditions (Paper
53
V). This is concluded using the results for the continuous discharge of acidic water,
as discussed previously. However, for long simulation times in small streams or
using procedures that increase the mass transfer process either by increasing
turbulence or the mass transfer area, the effect of 𝐶𝑂2 degassing and calcite
dissolution will have a significant contribution.
Despite the fact that the effects of carbon dioxide degassing and calcite
dissolution are negligible in the present hypothetical simulation, including the
influence of the surrounding environment using these processes in the model is
relevant due to their importance in natural waters (Polsenaere & Abril, 2012;
Ziemkiewicz, Skousen, Brant, & Lovett, 1997; Choi, Hulseapple, Conklin, M, &
Harvey, 1998; Zhai, Dai, & Guo, 2007; Jiang & Wang, 2008). Although widely
discussed, determination of mass transfer coefficients for these processes is quite
ambiguous and the values obtained using mass transfer handbooks models (Foust,
A., Clump, Maus, & Anderson, 1980; Treybal, 1981) differ from the ones obtained
in studies about degassing of CO2 in natural waters (Jiang & Wang, 2008; Zhai, Dai,
& Guo, 2007). Studies about more accurate and specific procedures to estimate mass
transfer coefficients is necessary for future development of the modelling
methodology.
54
Figure 25 Simulated results for continuous discharge of acidic water. a) pH is simulated without equilibrium adjustment as a conservative pollutant, where only advection and diffusion is considered. b) pH is simulated using advection-diffusion equation with equilibrium adjustment, CO2 degassing, and calcite dissolution. c) comparison of pH with and without equilibrium adjustment (Paper V).
a)
b)
4
4,5
5
5,5
6
6,5
7
7,5
8
8,5
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750
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975
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100
00
Str
eam
pH
Length (m)
0 min 30 min 60 min 90 min 120 min
4
4,5
5
5,5
6
6,5
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eam
pH
Length (m)
0 min 30 min 60 min 90 min 120 min
4
4,5
5
5,5
6
6,5
7
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8,5
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250
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750
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975
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00
Str
eam
pH
Length (m)
0 min 30 min 60 min 90 min 120 min
4
4,5
5
5,5
6
6,5
7
7,5
8
8,5
0
250
500
750
100
0
125
0
150
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175
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250
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900
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925
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950
0
975
0
100
00
Str
eam
pH
Length (m)
0 min 30 min 60 min 90 min 120 min
without equilibrium adjustment
with equilibrium adjustment
c)
55
Figure 26 Simulated results for non-continuous discharge of acidic water. a) pH is simulated without equilibrium adjustment as a conservative pollutant, where only advection and diffusion is considered. b) pH is simulated using advection-diffusion equation with equilibrium adjustment, CO2 degassing, and calcite dissolution. c) comparison of pH with and without equilibrium adjustment (Paper V).
a)
b)
4
4,5
5
5,5
6
6,5
7
7,5
8
8,5
0
250
500
750
100
0
125
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975
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eam
pH
Length
0 min 30 min 60 min 90 min 120 min
4
4,5
5
5,5
6
6,5
7
7,5
8
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0
975
0
100
00
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eam
pH
Length (m)
0 min 30 min 60 min 90 min 120 min
4
4,5
5
5,5
6
6,5
7
7,5
8
8,5
0
250
500
750
100
0
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975
0
100
00
Str
eam
pH
Length (m)
0 min 30 min 60 min 90 min 120 min
4
4,5
5
5,5
6
6,5
7
7,5
8
8,5
0
250
500
750
100
0
125
0
150
0
175
0
200
0
225
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250
0
275
0
300
0
325
0
350
0
375
0
400
0
425
0
450
0
475
0
500
0
525
0
550
0
575
0
600
0
625
0
650
0
675
0
700
0
725
0
750
0
775
0
800
0
825
0
850
0
875
0
900
0
925
0
950
0
975
0
100
00
Str
eam
pH
0 min 30 min 60 min 90 min 120 min
with equilibrium adjustment
without equilibrium adjustment
c)
56
4.4 Applicability and limitations of the models
All process based models proposed in this thesis are to be used in freshwater.
Freshwater means that the TDS or electrical conductivity should be below 1000
mg/L or 1500 μS/cm, respectively (Pacific, 2016; Walton, 1989). The reason for
this restriction is that, for sake of simplicity it was assumed that the activity
coefficients of chemical species in water are close to one; thus, the molar
concentration of an ion is assumed to be equal to its activity. The models are not
recommended for saline water such as seawater or saline lagoons. Usage of models
for saline water requires updating the molar concentrations to activities.
The Model 1 and Model 2 were developed to minimize the input data to be used,
while still yielding satisfactory estimates. This makes the models suitable for use in
developing countries, but also in developed countries when there is no need to have
very accurate information about the water quality obtained through sophisticated
and costly monitoring programs.
Model 1
The model is a simple tool that estimates the concentrations of major ions (𝑁𝑎+,
𝐾+, 𝑀𝑔2+, 𝐶𝑎2+, 𝐻𝐶𝑂3−, 𝑆𝑂4
2−, 𝐶𝑙−, and 𝑁𝑂3−) as well as some minor ions and
heavy metals (𝐹𝑒2+, 𝑀𝑛2+, 𝐶𝑑2+, 𝐶𝑢2+, 𝐴𝑙3+, 𝑃𝑑2+ and 𝑍𝑛2+) in rivers when the
𝑝𝐻, alkalinity, temperature, and electric conductivity are known (Paper II).
As discussed before, when using the generalized method, the model employs
continental averages for calibration, which may induce large uncertainties in the
results (Paper II). However, these uncertainties can be partly overcome by using the
customized method, which, instead of using continental averages, relies on baseline
data for the specific river. Even with the uncertainty introduced by the continental
averages, the concentrations of major ions estimated using the generalized method
are reasonably good, as previously shown, although it is important to consider the
recommended limits for DiffEC (difference between the measured and estimated in
relation to measured electrical conductivity in percentage). It should be noted that
all processes in the model are globally valid and therefore the use of Swedish data
for validation is not restriction.
Unfortunately, it was not possible to validate the predictive capability of the
model for several continents or countries, especially for developing countries where
the model is expected to be used, due to lack of data. This is something to be
investigated in the future; however, the model was tested using Swedish data and
gave good results.
There are many possibilities to further develop the model, such as including more
ions, finding different methods to estimate the minor ions and heavy metals that do
not use equilibrium concentrations, and including complex compounds in the model
estimates. All these improvements, however, require data and more detailed studies.
57
Model 2
The model is developed to simulate pH and alkalinity in streams. The model has
two main components, one for near field or mixing zone and other for far field. The
model for simulating pH and alkalinity in the near field, mixing zone was developed
considering carbonaceous alkalinity species and tested using laboratory data and an
extension for including the effect of iron was proposed but not tested (Paper IV,
Paper V). Although not tested using laboratory or field data a modelling
methodology for far field was proposed based on principles already validated in
previous studies and the quality of results were found qualitatively good based on
hypothetical simulation.
The main limitations of Model 2 are: (1) the model assumes instantaneous mixing
of acidic discharges and stream water, mixing in natural rivers is affected by river
width, depth, water velocity, roughness of the stream bed, and the ration between
the flow of the main stream and the acidic discharge; (2) the model cannot capture
zonation in wide and deep streams; and (3) the model can only be employed when
the purpose is to investigate the 𝑝𝐻 of rivers impacted by acidic discharge and no
detailed information about the concentrations of metals are required.
These limitations can be overcome by (1) using mixing theory and real data to
obtain mixing zone length; (2) including three-dimensional transport in the mixing
zone; and (3) including simulation of concentration of metals in the models.
a) Modelling pH and alkalinity in the near field
The model can be applied to simulate different scenarios of contamination of river
waters by acidic discharges in the near field, mixing zone (Paper IV). The model
allows simulation of contamination with two different approaches. The first
approach is to consider a change of 𝑝𝐻 in the acidic discharge, assuming constant
flow, and the second approach is to consider a change in the flow of acidic discharge
with constant 𝑝𝐻. In practice, the model can be used as a decision support tool by
authorities for granting new mining licenses, and by different industries that produce
acidic wastewaters to manage their discharges to the environment.
At the present stage, this model is limited because it includes only carbonaceous
alkalinity species; the effect of other alkalinity species, e.g. iron, manganese, and
aluminum are not considered although they would affect the results of the model
when dealing with water having 𝑝𝐻 below 4.3. However, the model approach can
be improved by (1) including more alkalinity species as well as the effect of iron,
manganese, and aluminum in the derivation of equation 32. Despite the limitations
of the model it can be used to get a first evaluation of the impact of acidic discharges
into rivers. The approach can be further developed to simulate extremely low 𝑝𝐻
cases, such as Iron Mountain in California by expanding equation 38 (Nordstrom,
Alpers, Ptacek, & Blowes, 2000).
58
b) Modelling pH and alkalinity in the far field
A modelling methodology is suggested which can be used to simulate different
types of contamination of water which includes acidification and reclamation of
streams already impacted by acidic discharges (Paper V). Both continuous and non-
continuous discharge of acidic water can be simulated. The modelling methodology
can be used by both water quality monitoring authorities and industries. Water
quality monitoring authorities can use the modelling for simulating acidification or
reclamation of streams. Simulating acidification or reclamation of streams allow
allocating resources where there is high risk of impacts. Appropriate allocation of
resources is particularly important in developing countries where the resources are
limited. The industries can use the model for managing their acidic discharges to
the environment.
The model is not tested with real data because of its complexity. Parts and
processes of the model must be investigated and optimized separately, before testing
the full model to simulate real conditions. The parts and processes include: mass
transfer coefficients for 𝐶𝑂2 degassing and calcite dissolution; defining appropriate
method for estimating the mas transfer and dispersion coefficients. Also in order to
improve the model all ions which may affect significantly the alkalinity when there
is acid mine drainage should be included.
59
5.Conclusions and recommendations
A water quality monitoring system is proposed for the Zambezi River Basin in
Mozambique. It has the following characteristics: (1) produces consistent and
comparable water quality information; (2) provides feedback to outcomes and goals
of the government; and (3) is implemented in a way that allows continuous
improvement of water quality information produced, in the context of mining
development, and under the constraint of lack of human and financial resources. The
system includes two alternative monitoring procedures. One procedure that consists
of improving the current situation, which is characterized by multiple actors doing
monitoring in isolation, by standardizing the analytical methods and improving data
sharing through a common web-based reporting system. The other proposed
monitoring procedure is a centralized approach, which consists on having a
consulting company doing the monitoring for the whole river basin in Mozambique.
The second option has the advantages of improving consistency and comparability
of the data, thereby allowing for more accurate trend analyses. However, it would
probably be a challenge to convince all stakeholders to have the same consulting
company doing the water quality monitoring. It is concluded that the best way
forward is to implement the first procedure and slowly move to the second.
One of the major issues of water quality in rivers impacted by mining is acid mine
drainage. Acid mine drainage impacts both surface and ground water. When acid
mine drainage impacts a water body, it lowers the 𝑝𝐻 and causes an instant threat
to the biota and the ecological balance.
Models can be used together with the water quality monitoring system suggested
for Zambezi River basin to reduce the overall monitoring cost. Modelling of
groundwater contamination due to mining is more common than surface water,
while human activities and biodiversity are mainly based on surface water; thus,
modelling in this thesis focuses on surface water. Models are to be used both for (1)
estimating water quality parameters that are difficult and costly to measure and for
(2) simulating acidification or reclamation of streams already impacted by acidic
discharges allowing to allocate resources to areas with high risk of pollution. Being
able to allocate resources in areas at high risk of pollution is important for
developing countries because the resources are limited.
60
Analysed water quality models are limited to simulate pH and alkalinity in streams
impacted by acid mine drainage. Models such as OITS and PHREEQ C can simulate
mixing and transport of non-conservative pollutant but they fail when the task is to
simulate pH which is influenced by equilibrium reactions between the alkalinity
species and interaction with the surrounding environment simultaneously. As the
pH influences solubility of minerals in the stream, thus affecting greatly the
concentration of inorganic solutes, it is also useful to have a model that estimate
other water quality parameters based on pH.
Two models were developed: (1) to estimate the concentration of inorganic ions
based on pH, alkalinity, and temperature, thus reducing the cost of sampling and
analysis; and (2) to simulate pH and alkalinity in streams impacted by acidic
discharges, thus allowing for allocating properly the human and financial resources.
Major ions (𝑁𝑎+, 𝐾+, 𝑀𝑔2+, 𝐶𝑎2+, 𝐻𝐶𝑂3−, 𝑆𝑂4
2−, 𝐶𝑙−, and 𝑁𝑂3−) together with the
maximum possible concentrations of minor ions and heavy metals (𝐹𝑒2+, 𝑀𝑛2+,
𝐶𝑑2+, 𝐶𝑢2+, 𝐴𝑙3+, 𝑃𝑑2+ and 𝑍𝑛2+) are estimated based on pH, alkalinity and
temperature using a physical processes based model. The model performance was
compared with artificial neural networks which yielded slightly better results than
the physical processes based model. However, the physical process based model has
the advantage of not requiring historical data. It also has a way of evaluating the
quality of results through comparison of the measured and estimated electric
conductivity based on modelled results of concentration of major ions making it
favourable to be used in developing countries where there is a lack of historical data.
A simple and easy-to-use physical process based model that simulates pH and
alkalinity considering equilibrium between the alkalinity species in water was
developed to overcome the limitations of available models for simulating
acidification of streams. Simulation of pH and alkalinity in the near field, mixing
zone considering only carbonaceous alkalinity was tested using laboratory data and
it was concluded that it yields satisfactory results. Further, an extension of the model
to include iron (III) effect on alkalinity in the near field was demonstrated and, a
modelling methodology for simulating 𝑝𝐻 and alkalinity in the far field was
proposed. Although, not tested quantitatively using laboratory or field data the
modelling approach is based on already tested principles and the results obtained
from a hypothetical simulation behave qualitatively as expected. Calibration, by
adjusting modelling parameters such as dispersion and mass transfer coefficients
will be necessary before practical application.
61
6.Future work
There is a need of promoting the use of the water quality monitoring system and the
models presented in this thesis. The system and the models are expected to be used
in Mozambique and other places with similar conditions; i.e. in developing countries
with potential environmental problems due to mining. The results of this study will
be shared with the Mozambican government water quality monitoring authorities.
The system and the models might be optimized to fulfil the actual needs of
government authorities. However, with some improvements the models developed
in this study can be used also in developed countries to make the water quality
monitoring programs and reclamation of streams impacted by acidic discharges
more sustainable.
Activities planned for future development of the models include for Model 1 –
(using pH, alkalinity, and temperature to estimate the concentration of major ions):
(1) design of a water quality monitoring device that measures pH, alkalinity,
temperature and electric conductivity and uses the model to estimate the
concentration of major ions as well as evaluating the water quality change based on
the value of DiffEC (difference between measured and estimated with relation to
measured electric conductivity); Model 2 - (Modelling pH and alkalinity in stream):
(1) include more ions that influence alkalinity for simulating mixing and test it using
laboratory and real data; (2) conduct study about the mass transfer coefficients for
dissolution of some minerals and gases such as calcite, gypsum and carbon dioxide;
(3) conduct study about appropriate space step to perform simulation; (4) investigate
the length of mixing zone as function of river conditions, such as water velocity,
stream depth and roughness as well as the influence of dissolution of solid materials
at the bottom of the stream and gas exchange with the atmosphere; (5) test the full
optimized model using laboratory and field data.
The final task will be combining model 1 and 2. The water quality monitoring device
that contains model 1 is to be used to generate input data for model 2. During
simulation of contamination or reclamation using model 2, model 1 can also be
used to get speciation of water in terms of inorganic ions. The models 1 and 2 will
be combined to produce a computer software that simulates contamination by acidic
water or reclamation of already impacted streams, providing both pH and alkalinity
values and concentration of inorganic ions.
62
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